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Effective descent morphisms, originally defined in Grothendieck descent theory, form a class of special morphisms within a category. Essentially, an effective descent morphism enables bundles over its codomain to be fully described as bundles over its domain endowed with additional algebraic structure, called descent data. Like the study of epimorphisms, studying effective descent morphisms is interesting in its own right, providing deeper insights into the category under consideration. Moreover, studying these morphisms is part of the foundations of several applications of descent theory, notably including Janelidze-Galois theory, also known as categorical Galois theory. Traditionally, the study of effective descent morphisms has focused on investigating and exploiting the reflection properties of certain functors. In contrast, we introduce a novel approach by establishing general results on the preservation of effective descent morphisms. We demonstrate that these preservation results enhance the toolkit for studying such morphisms, by observing that all Grothendieck (op)fibrations satisfying mild conditions fit our framework. To illustrate these findings, we provide several examples of Grothendieck (op)fibrations that preserve effective descent morphisms, including topological functors and other forgetful functors of significant interest in the literature.

We study the categorical structure of the Grothendieck construction of an indexed category $\mathcal{L}:\mathcal{C}^{op}\to\mathbf{CAT}$ and characterise fibred limits, colimits, and monoidal structures. Next, we give sufficient conditions for the monoidal closure of the total category $\Sigma_\mathcal{C} \mathcal{L}$ of a Grothendieck construction of an indexed category $\mathcal{L}:\mathcal{C}^{op}\to\mathbf{CAT}$. Our analysis is a generalization of G\"odel's Dialectica interpretation, and it relies on a novel notion of $\Sigma$-tractable monoidal structure. As we will see, $\Sigma$-tractable coproducts simultaneously generalize cocartesian coclosed structures, biproducts and extensive coproducts. We analyse when the closed structure is fibred -- usually it is not.

We investigate the properties of lax comma categories over a base category $X$, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from $\mathsf{Cat}//X$ to $\mathsf{Cat}$ is topological if and only if $X$ is large-complete. Moreover, we provide conditions for $\mathsf{Cat}//X$ to be complete, cocomplete, extensive and cartesian closed. We analyze descent in $\mathsf{Cat}//X$ and identify necessary conditions for effective descent morphisms. Our findings contribute to the literature on lax comma categories and provide a foundation for further research in 2-dimensional Janelidze's Galois theory., Comment: 13 pages

We consider the canonical pseudodistributive law between various free limit completion pseudomonads and the free coproduct completion pseudomonad. When the class of limits includes pullbacks, we show that this consideration leads to notions of extensive categories. More precisely, we show that extensive categories with pullbacks and infinitary lextensive categories are the pseudoalgebras for the pseudomonads resulting from the pseudodistributive laws. Moreover, we introduce the notion of doubly-infinitary lextensive category, and we establish that the freely generated such categories are cartesian closed. From this result, we further deduce that, in freely generated infinitary lextensive categories, the objects with a finite number of connected components are exponentiable. We conclude our work with remarks on descent theoretical aspects of this work, along with results concerning non-canonical isomorphisms, and relationship with other work., Comment: 18 pages

Disentangling the radio flux contribution from star formation (SF) and active-galactic-nuclei (AGN) activity is a long-standing problem in extragalactic astronomy, since at frequencies of $\lesssim$ 10 GHz, both processes emit synchrotron radiation. We present in this work the general objectives of the PARADIGM Project, a multi-instrument concept to explore star-formation and mass assembly of galaxies. We introduce two novel general approaches for a detailed multiscale study of the radio emission in local U/LIRGs. In this work, we use archival interferometric data from the Very Large Array (VLA) centred at ~ 6 GHz (C band) and present new observations from the e-Multi-Element Radio-Linked Interferometer Network (e-MERLIN) for UGC5101, VV705, VV250 and UGC8696. Using our image decomposition methods, we robustly disentangle the radio emission into distinct components by combining information from the two interferometric arrays. We use e-MERLIN as a probe of the core-compact radio emission (AGN or starburst) at ~ 20 pc scales, and as a probe of nuclear diffuse emission, at scales ~ 100 - 200 pc. With VLA, we characterise the source morphology and the flux density on scales from 200 pc up to and above 1 kpc. As a result, we find deconvolved and convolved sizes for nuclear regions from ~ 10 pc to ~ 200 pc. At larger scales, we find sizes of 1.5 - 2 kpc for diffuse structures (with effective sizes of ~ 300 - 400 pc). We demonstrate that the radio emission from nuclear extended structures (~ 100 pc) can dominate over core-compact components, providing a significant fraction of the total multiscale SF output. We establish a multiscale radio tracer for star formation by combining information from different instruments. Consequently, this work sets a starting point to potentially correct for overestimations of AGN fractions and underestimates of SF activity., Comment: Accepted for publication in MNRAS. 31 pages (9 pages appendix), 13 figures, 9 tables. Online code repository: morphen - https://github.com/lucatelli/morphen

We delve into the concept of categories with products that distribute over coproducts, which we call doubly-infinitary distributive categories. We show various instances of doubly-infinitary distributive categories aiming for a comparative analysis with established notions such as extensivity, infinitary distributiveness, and cartesian closedness. Our exploration reveals that this condition represents a substantial extension beyond the classical understanding of infinitary distributive categories. Our main theorem establishes that free doubly-infinitary distributive categories are cartesian closed. We end the paper with remarks on non-canonical isomorphisms, open questions, and future work., Comment: 16 pages, minor, corrected some typos, added references

Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite limits, we construct an adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon \mathsf{Cat}(T,\mathcal V) \to (\overline T, \mathcal V)\text{-}\mathsf{Cat} $ between categories of generalized enriched multicategories and generalized internal multicategories, provided the monad $ T $ satisfies a suitable condition, which is satisfied by several examples. We verify, moreover, that the left adjoint is fully faithful, and preserves pullbacks, provided that the copower functor $ - \boldsymbol{\cdot} 1 \colon \mathsf{Set} \to \mathcal V $ is fully faithful. We also apply this result to study descent theory of generalized enriched multicategorical structures. These results are built upon the study of base-change for generalized multicategories, which, in turn, was carried out in the context of categories of horizontal lax algebras arising out of a monad in a suitable 2-category of pseudodouble categories., Comment: 72 pages, final version to appear in Appl. Categ. Structures

We present the results of a size and structural analysis of 1395 galaxies at $0.5 \leq z \lesssim 8$ with stellar masses $\log \left(M_* / M_{\odot}\right)$ $>$ 9.5 within the JWST Public CEERS field that overlaps with the HST CANDELS EGS observations. We use GALFIT to fit single S\'ersic models to the rest-frame optical profile of our galaxies, which is a mass-selected sample complete to our redshift and mass limit. Our primary result is that at fixed rest-frame wavelength and stellar mass, galaxies get progressively smaller, evolving as $\sim (1+z)^{-0.71\pm0.19}$ up to $z \sim 8$. We discover that the vast majority of massive galaxies at high redshifts have low S\'ersic indices, thus do not contain steep, concentrated light profiles. Additionally, we explore the evolution of the size-stellar mass relationship, finding a correlation such that more massive systems are larger up to $z \sim 3$. This relationship breaks down at $z > 3$, where we find that galaxies are of similar sizes, regardless of their star formation rates and S\'ersic index, varying little with mass. We show that galaxies are more compact at redder wavelengths, independent of sSFR or stellar mass up to $z \sim 3$. We demonstrate the size evolution of galaxies continues up to $z \sim 8$, showing that the process or causes for this evolution is active at early times. We discuss these results in terms of ideas behind galaxy formation and evolution at early epochs, such as their importance in tracing processes driving size evolution, including minor mergers and AGN activity., Comment: Submitted to MNRAS

Let $\mathsf{Ord} $ be the category of (pre)ordered sets. Unlike $\mathsf{Ord}/X$, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category $\mathsf{Ord} //X$. In this paper we show that the forgetful functor $\mathsf{Ord} //X\to \mathsf{Ord} $ is topological if and only if $X$ is complete. Moreover, under suitable hypothesis, $\mathsf{Ord} // X$ is complete and cartesian closed if and only if $X$ is. We end by analysing descent in this category. Namely, when $X$ is complete and cartesian closed, we show that, for a morphism in $\mathsf{Ord} //X$, being pointwise effective for descent in $\mathsf{Ord} $ is sufficient, while being effective for descent in $\mathsf{Ord} $ is necessary, to be effective for descent in $\mathsf{Ord} //X$., Comment: 12 pages

For any suitable base category $\mathcal{V} $, we find that $\mathcal{V} $-fully faithful lax epimorphisms in $\mathcal{V} $-$\mathsf{Cat} $ are precisely those $\mathcal{V}$-functors $F \colon \mathcal{A} \to \mathcal{B}$ whose induced $\mathcal{V} $-functors $\mathsf{Cauchy} F \colon \mathsf{Cauchy} \mathcal{A} \to \mathsf{Cauchy} \mathcal{B} $ between the Cauchy completions are equivalences. For the case $\mathcal{V} = \mathsf{Set} $, this is equivalent to requiring that the induced functor $\mathsf{CAT} \left( F,\mathsf{Cat}\right) $ between the categories of split (op)fibrations is an equivalence. By reducing the study of effective descent functors with respect to the indexed category of split (op)fibrations $\mathcal{F}$ to the study of the codescent factorization, we find that these observations on fully faithful lax epimorphisms provide us with a characterization of (effective) $\mathcal{F}$-descent morphisms in the category of small categories $\mathcal{Cat}$; namely, we find that they are precisely the (effective) descent morphisms with respect to the indexed categories of discrete opfibrations -- previously studied by Sobral. We include some comments on the Beck-Chevalley condition and future work., Comment: 8 pages, revised version, 11-01-2023

We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can be used to give a very straightforward proof of correctness of practical forward- and reverse-mode dual numbers style automatic differentiation (AD) on ML-family languages. The key idea is to combine it with a suitable open logical relations technique for reasoning about differentiable partial functions (a suitable lifting of the partiality monad to logical relations), which we introduce., Comment: 25 pages (18 pages + references and appendices), conference paper (the corresponding extended work can be found at arXiv:2210.07724), submitted to FoSSaCS. arXiv admin note: substantial text overlap with arXiv:2210.07724

We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD) correctness: namely, we present a correctness proof of a dual numbers style AD code transformation for realistic functional languages in the ML-family. We also show how this code transformation provides us with correct forward- and reverse-mode AD. The starting point is to interpret a functional programming language as a suitable freely generated categorical structure. In this setting, by the universal property of the syntactic categorical structure, the dual numbers AD code transformation and the basic $\omega$-cpo semantics arise as structure preserving functors. The proof follows, then, by a novel logical relations argument. The key to much of our contribution is a powerful monadic logical relations technique for term recursion and recursive types. It provides us with a semantic correctness proof based on a simple approach for denotational semantics, making use only of the very basic concrete model of $\omega$-cpos.

We present results on the morphological and structural evolution of a total of 4265 galaxies observed with JWST at $1.5 < z < 8$ in the JWST CEERS observations that overlap with the CANDELS EGS field. This is the biggest visually classified sample observed with JWST yet, $\sim20$ times larger than previous studies, and allows us to examine in detail how galaxy structure has changed over this critical epoch. All sources were classified by six individual classifiers using a simple classification scheme aimed to produce disk/spheroid/peculiar classifications, whereby we determine how the relative number of these morphologies evolves since the Universe's first billion years. Additionally, we explore structural and quantitative morphology measurements using \textsc{Morfometryka}, and show that galaxies at $z > 3$ are not dominated by irregular and peculiar structures, either visually or quantitatively, as previously thought. We find a strong dominance of morphologically selected disk galaxies up to $z = 8$, a far higher redshift than previously thought possible. We also find that the stellar mass and star formation rate densities are dominated by disk galaxies up to $z \sim 6$, demonstrating that most stars in the universe were likely formed in a disk galaxy. We compare our results to theory to show that the fraction of types we find is predicted by cosmological simulations, and that the Hubble Sequence was already in place as early as one billion years after the Big Bang. Additionally, we make our visual classifications public for the community., Comment: 18 pages, 13 figures. Submitted to ApJ; Comments welcome, Classification data will be publicly available at https://github.com/astroferreira/CEERS_JUNE_VISUAL_CLASSIFICATIONS when paper is in press

The various Euclid imaging surveys will become a reference for studies of galaxy morphology by delivering imaging over an unprecedented area of 15 000 square degrees with high spatial resolution. In order to understand the capabilities of measuring morphologies from Euclid-detected galaxies and to help implement measurements in the pipeline, we have conducted the Euclid Morphology Challenge, which we present in two papers. While the companion paper by Merlin et al. focuses on the analysis of photometry, this paper assesses the accuracy of the parametric galaxy morphology measurements in imaging predicted from within the Euclid Wide Survey. We evaluate the performance of five state-of-the-art surface-brightness-fitting codes DeepLeGATo, Galapagos-2, Morfometryka, Profit and SourceXtractor++ on a sample of about 1.5 million simulated galaxies resembling reduced observations with the Euclid VIS and NIR instruments. The simulations include analytic S\'ersic profiles with one and two components, as well as more realistic galaxies generated with neural networks. We find that, despite some code-specific differences, all methods tend to achieve reliable structural measurements (10% scatter on ideal S\'ersic simulations) down to an apparent magnitude of about 23 in one component and 21 in two components, which correspond to a signal-to-noise ratio of approximately 1 and 5 respectively. We also show that when tested on non-analytic profiles, the results are typically degraded by a factor of 3, driven by systematics. We conclude that the Euclid official Data Releases will deliver robust structural parameters for at least 400 million galaxies in the Euclid Wide Survey by the end of the mission. We find that a key factor for explaining the different behaviour of the codes at the faint end is the set of adopted priors for the various structural parameters., Comment: Accepted by A&A. 30 pages, 23+6 figures, Euclid pre-launch key paper. Companion paper: Euclid Collaboration XXV: Merlin et al. 2022 Minor corrections after journal review

The ESA Euclid mission will provide high-quality imaging for about 1.5 billion galaxies. A software pipeline to automatically process and analyse such a huge amount of data in real time is being developed by the Science Ground Segment of the Euclid Consortium; this pipeline will include a model-fitting algorithm, which will provide photometric and morphological estimates of paramount importance for the core science goals of the mission and for legacy science. The Euclid Morphology Challenge is a comparative investigation of the performance of five model-fitting software packages on simulated Euclid data, aimed at providing the baseline to identify the best suited algorithm to be implemented in the pipeline. In this paper we describe the simulated data set, and we discuss the photometry results. A companion paper (Euclid Collaboration: Bretonni\`ere et al. 2022) is focused on the structural and morphological estimates. We created mock Euclid images simulating five fields of view of 0.48 deg2 each in the $I_E$ band of the VIS instrument, each with three realisations of galaxy profiles (single and double S\'ersic, and 'realistic' profiles obtained with a neural network); for one of the fields in the double S\'ersic realisation, we also simulated images for the three near-infrared $Y_E$, $J_E$ and $H_E$ bands of the NISP-P instrument, and five Rubin/LSST optical complementary bands ($u$, $g$, $r$, $i$, and $z$). To analyse the results we created diagnostic plots and defined ad-hoc metrics. Five model-fitting software packages (DeepLeGATo, Galapagos-2, Morfometryka, ProFit, and SourceXtractor++) were compared, all typically providing good results. (cut), Comment: 29 pages, 33 figures. Euclid pre-launch key paper. Companion paper: Bretonniere et al. 2022

The miniJPAS is a 1 deg$^2$ survey that uses the Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) filter system (54 narrow-band filters) with the Pathfinder camera. We study mJPC2470-1771, the most massive cluster detected in miniJPAS. We study the stellar population properties of the members, their star formation rates (SFR), star formation histories (SFH), the emission line galaxy (ELG) population, their spatial distribution, and the effect of the environment on them, showing the power of J-PAS to study the role of environment in galaxy evolution. We use a spectral energy distribution (SED) fitting code to derive the stellar population properties of the galaxy members: stellar mass, extinction, metallicity, colours, ages, SFH (a delayed-$\tau$ model), and SFRs. Artificial Neural Networks are used for the identification of the ELG population through the detection of H$\alpha$, [NII], H$\beta$, and [OIII] nebular emission. We use the WHAN and BPT diagrams to separate them into star-forming galaxies and AGNs. We find that the fraction of red galaxies increases with the cluster-centric radius. We select 49 ELG, 65.3\% of the them are probably star forming galaxies, and they are dominated by blue galaxies. 24% are likely to host an AGN (Seyfert or LINER galaxies). The rest are difficult to classify and are most likely composite galaxies. Our results are compatible with an scenario where galaxy members were formed roughly at the same epoch, but blue galaxies have had more recent star formation episodes, and they are quenching from inside-out of the cluster centre. The spatial distribution of red galaxies and their properties suggest that they were quenched prior to the cluster accretion or an earlier cluster accretion epoch. AGN feedback and/or mass might also be intervening in the quenching of these galaxies., Comment: 24 pages, 17 figures, 4 tables, accepted in Astronomy & Astrophysics

The photometric and morphological analysis of galaxies in clusters provides invaluable information regarding the evolutionary stage of the cluster itself. In addition, it helps to understand how the environment affects the properties of the galaxies and, as a consequence, their evolutionary path. In this contribution we present the first steps on the photometric and morphological analysis of galaxies in the Fornax cluster using S-PLUS data. We expect that the S-PLUS novel filter set and wide field coverage allow us to obtain new information about Fornax and its galaxy population., Comment: 3 pages, 5 figures. Accepted to be published in Bolet\'in de la Asociaci\'on Argentina de Astronom\'ia

We give sufficient conditions for effective descent in categories of (generalized) internal multicategories. Two approaches to study effective descent morphisms are pursued. The first one relies on establishing the category of internal multicategories as an equalizer of categories of diagrams. The second approach extends the techniques developed by Ivan Le Creurer in his study of descent for internal essentially algebraic structures., Comment: 19 pages

We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featuring the combination of - tuple types; - sum types; - inductive types; - coinductive types; - function types. We achieve this by analysing the categorical semantics of such types in $\Sigma$-types (Grothendieck constructions) of suitable categories. Using a novel categorical logical relations technique for such expressive type systems, we give a correctness proof of CHAD in this setting by showing that it computes the usual mathematical derivative of the function that the original program implements. The result is a principled, purely functional and provably correct method for performing forward and reverse mode automatic differentiation (AD) on total functional programming languages with expressive type systems., Comment: Under review at MSCS

We study lax epimorphisms in 2-categories, with special attention to $\mathsf{Cat}$ and $\mathcal{V}$-$\mathsf{Cat}$. We show that any 2-category with convenient colimits has an orthogonal $LaxEpi$-factorization system, and we give a concrete description of this factorization in $\mathsf{Cat}$.

The morphological diversity of galaxies is a relevant probe of galaxy evolution and cosmological structure formation, but the classification of galaxies in large sky surveys is becoming a significant challenge. We use data from the Stripe-82 area observed by the Southern Photometric Local Universe Survey (S-PLUS) in twelve optical bands, and present a catalogue of the morphologies of galaxies brighter than $r=17$ mag determined both using a novel multi-band morphometric fitting technique and Convolutional Neural Networks (CNNs) for computer vision. Using the CNNs we find that, compared to our baseline results with 3 bands, the performance increases when using 5 broad and 3 narrow bands, but is poorer when using the full $12$ band S-PLUS image set. However, the best result is still achieved with just 3 optical bands when using pre-trained network weights from an ImageNet data set. These results demonstrate the importance of using prior knowledge about neural network weights based on training in unrelated, extensive data sets, when available. Our catalogue contains 3274 galaxies in Stripe-82 that are not present in Galaxy Zoo 1 (GZ1), and we also provide our classifications for 4686 galaxies that were considered ambiguous in GZ1. Finally, we present a prospect of a novel way to take advantage of $12$ band information for morphological classification using morphometric features, and we release a model that has been pre-trained on several bands that could be adapted for classifications using data from other surveys. The morphological catalogues are publicly available., Comment: accepted version for publication in MNRAS

A detailed study of the morphology of lenticular galaxies is an important way to understand how this type of galaxy formed and evolves over time. Decomposing a galaxy into its components (disc, bulge, bar, ...) allows recovering the colour gradients present in each system, its star formation history, and its assembly history. We use GALFITM to perform a multi-wavelength structural decomposition of the closest lenticular galaxy, NGC 3115, resulting in the description of its stellar light into several main components: a bulge, a thin disc, a thick disc and also evidence of a bar. We report the finding of central bluer stellar populations in the bulge, as compared to the colour of the galaxy outskirts, indicating either the presence of an Active Galactic Nucleus (AGN) and/or recent star formation activity. From the spectral energy distribution results, we show that the galaxy has a low luminosity AGN component, but even excluding the effect of the nuclear activity, the bulge is still bluer than the outer-regions of the galaxy, revealing a recent episode of star formation. Based on all of the derived properties, we propose a scenario for the formation of NGC 3115 consisting of an initial gas-rich merger, followed by accretions and feedback that quench the galaxy, until a recent encounter with the companion KK084 that reignited the star formation in the bulge, provoked a core displacement in NGC 3115 and generated spiral-like features. This result is consistent with the two-phase formation scenario, proposed in previous studies of this galaxy., Comment: Accepted for publication in MNRAS: 22 pages, 15 figures, 7 tables, 1 appendix

This work is a Brazilian-Indian collaboration. It aims at investigating the structuralproperties of Lenticular galaxies in the Stripe 82 using a combination of S-PLUS (Southern Photometric Local Universe Survey) and SDSS data. S-PLUS is a noveloptical multi-wavelength survey which will cover nearly 8000 square degrees of the Southern hemisphere in the next years and the first data release covers the Stripe 82 area. The morphological classification and study of the galaxies' stellar population will be performed combining the Bayesian Spectral type (from BPZ) and Morfometryka (MFMTK) parameters. BPZ and MFMTK are two complementary techniques, since the first one determines the most likely stellar population of a galaxy, in order to obtain its photometric redshift (phot-z), and the second one recovers non-parametric morphological quantities, such as asymmetries and concentration. The combination ofthe two methods allows us to explore the correlation between galaxies shapes (smooth, with spiral arms, etc.) and their stellar contents (old or young population). The preliminary results, presented in this work, show how this new data set opens a new window on our understanding of the nearby universe.

We explore the morphometric properties of a group of 73 ram pressure stripping candidates in the A901/A902 multi-cluster system, at z$\sim$0.165, to characterise the morphologies and structural evolution of jellyfish galaxies. By employing a quantitative measurement of morphometric indicators with the algorithm \textsc{morfometryka} on Hubble Space Telescope (F606W) images of the galaxies, we present a novel morphology-based method for determining trail vectors. We study the surface brightness profiles and curvature of the candidates and compare the results obtained with two analysis packages, \textsc{morfometryka} and \textsc{iraf/ellipse} on retrieving information of the irregular structures present in the galaxies. Our morphometric analysis shows that the ram pressure stripping candidates have peculiar concave regions in their surface brightness profiles. Therefore, these profiles are less concentrated (lower S\'ersic indices) than other star forming galaxies that do not show morphological features of ram pressure stripping. In combination with morphometric trail vectors, this feature could both help identify galaxies undergoing ram-pressure stripping and reveal spatial variations in the star formation rate., Comment: MNRAS accepted, 15 pages, 8 figures

The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will soon start to scan thousands of square degrees of the northern extragalactic sky with a unique set of $56$ optical filters from a dedicated $2.55$m telescope, JST, at the Javalambre Astrophysical Observatory. Before the arrival of the final instrument (a 1.2 Gpixels, 4.2deg$^2$ field-of-view camera), the JST was equipped with an interim camera (JPAS-Pathfinder), composed of one CCD with a 0.3deg$^2$ field-of-view and resolution of 0.23 arcsec pixel$^{-1}$. To demonstrate the scientific potential of J-PAS, with the JPAS-Pathfinder camera we carried out a survey on the AEGIS field (along the Extended Groth Strip), dubbed miniJPAS. We observed a total of $\sim 1$ deg$^2$, with the $56$ J-PAS filters, which include $54$ narrow band (NB, $\rm{FWHM} \sim 145$Angstrom) and two broader filters extending to the UV and the near-infrared, complemented by the $u,g,r,i$ SDSS broad band (BB) filters. In this paper we present the miniJPAS data set, the details of the catalogues and data access, and illustrate the scientific potential of our multi-band data. The data surpass the target depths originally planned for J-PAS, reaching $\rm{mag}_{\rm {AB}}$ between $\sim 22$ and $23.5$ for the NB filters and up to $24$ for the BB filters ($5\sigma$ in a $3$~arcsec aperture). The miniJPAS primary catalogue contains more than $64,000$ sources extracted in the $r$ detection band with forced photometry in all other bands. We estimate the catalogue to be complete up to $r=23.6$ for point-like sources and up to $r=22.7$ for extended sources. Photometric redshifts reach subpercent precision for all sources up to $r=22.5$, and a precision of $\sim 0.3$% for about half of the sample. (Abridged), Comment: The miniJPAS data and associated value added catalogues are publicly accessible via this url: http://archive.cefca.es/catalogues/minijpas-pdr201912

This paper is a contribution towards a two dimensional extension of the basic ideas and results of Janelidze-Galois theory. In the present paper, we give a suitable counterpart notion to that of \textit{absolute admissible Galois structure} for the lax idempotent context, compatible with the context of \textit{lax orthogonal factorization systems}. As part of this work, we study lax comma $2$-categories, giving analogue results to the basic properties of the usual comma categories. We show that each morphism of a $2$-category induces a $2$-adjunction between lax comma $2$-categories and comma $2$-categories, playing the role of the usual \textit{change of base functors}. With these induced $2$-adjunctions, we are able to show that each $2$-adjunction induces $2$-adjunctions between lax comma $2$-categories and comma $2$-categories, which are our analogues of the usual lifting to the comma categories used in Janelidze-Galois theory. We give sufficient conditions under which these liftings are $2$-premonadic and induce a lax idempotent $2$-monad, which corresponds to our notion of $2$-admissible $2$-functor. In order to carry out this work, we analyse when a composition of $2$-adjunctions is a lax idempotent $2$-monad, and when it is $2$-premonadic. We give then examples of our $2$-admissible $2$-functors (and, in particular, simple $2$-functors), specially using a result that says that all admissible ($2$-)functors in the classical sense are also $2$-admissible (and hence simple as well). We finish the paper relating coequalizers in lax comma $2$-categories and Kan extensions., Comment: 43 pages, new version

In this work we introduce the curvature of a galaxy brightness profile to identify its structural subcomponents in a non-parametrically fashion. Bulges, bars, disks, lens, rings and spiral arms are key to understand the formation and evolution path the galaxy undertook. Identifying them is also crucial for morphological classification of galaxies. We measure and analyse in detail the curvature of $14$ galaxies with varied morphology. High (low) steepness profiles show high (low) curvature measures. Transitions between components are identified as local peaks oscillations in the values of the curvature. We identify patterns that characterise bulges (pseudo or classic), disks, bars and rings. This method can be automated to identify galaxy components in large datasets or to provide a reliable starting point for traditional multicomponent modelling of galaxy light distribution., Comment: 21 pages, 19 figures. Accepted for publication in MNRAS

The fundamental construction underlying descent theory, the lax descent category, comes with a functor that forgets the descent data. We prove that, in any $2$-category $\mathfrak{A} $ with lax descent objects, the forgetful morphisms create all Kan extensions that are preserved by certain morphisms. As a consequence, in the case $\mathfrak{A} = \mathsf{Cat} $, we get a monadicity theorem which says that a right adjoint functor is monadic if and only if it is, up to the composition with an equivalence, (naturally isomorphic to) a functor that forgets descent data. In particular, within the classical context of descent theory, we show that, in a fibred category, the forgetful functor between the category of internal actions of a precategory $a$ and the category of internal actions of the underlying discrete precategory is monadic if and only if it has a left adjoint. More particularly, this shows that one of the implications of the celebrated Benabou-Roubaud theorem does not depend on the so called Beck-Chevalley condition. Namely, we prove that, in indexed categories, whenever an effective descent morphism induces a right adjoint functor, the induced functor is monadic., Comment: 32 pages

Let $\mathbb{A}$ be a $2$-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism $p$ exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the higher cokernel of $p$ is up to isomorphism the same as the semantic factorization of $p$, either one existing if the other does. The result can be seen as a counterpart account to the celebrated B\'{e}nabou-Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of $p$ trivially hold whenever $p$ has a left adjoint and, hence, in this case, we find monadicity to be a $2$-dimensional exact condition on $p$, namely, to be an effective faithful morphism of the $2$-category $\mathbb{A} $., Comment: Minor changes. 48 pages