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This work focuses on establishing the relationship between bipolar fuzzy automata, reverse bipolar fuzzy automata, and double bipolar fuzzy automata. It also introduces the concepts of bipolar fuzzy subsystems, reverse bipolar fuzzy subsystems, and double bipolar fuzzy subsystems, and explores various properties associated with these subsystems. Furthermore, the paper aims to introduce the categorical aspects of bipolar fuzzy automata and reverse bipolar fuzzy automata, along with their functorial relationship. [ABSTRACT FROM AUTHOR]

We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension. [ABSTRACT FROM AUTHOR]

We study the deformation complex of the natural morphism from the degree |$d$| shifted Lie operad to its polydifferential version, and prove that it is quasi-isomorphic to the Kontsevich graph complex |$\textbf {GC}_{d}$|⁠. In particular, we show that in the case |$d=2$| the Grothendieck–Teichmüller group |$\textbf {GRT}_{1}$| is a symmetry group (up to homotopy) of the aforementioned morphism. We also prove that in the case |$d=1$|⁠ , corresponding to the usual Lie algebras, the natural morphism admits a unique homotopy non-trivial deformation, which is described explicitly with the help of the universal enveloping construction. Finally, we prove the rigidity of the strongly homotopy version of the universal enveloping functor in the Lie theory. [ABSTRACT FROM AUTHOR]

In this paper first we construct the Eilenberg-MacLane space through Moore space then we study this space through an infinite symmetric product functor. Finally, we study some applications. [ABSTRACT FROM AUTHOR]

Given some links between Lyndon's Interpolation Theorem, term distribution, and Sommers and Englebretsen's logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen's Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the action for topological groupoids. In our work, some definitions and propositions are introduced and in addition to the basic construction of topological groupoid which are needed and we studied the different properties of categories and the properties of topological groupoid, and we define concepts such as topos, functor and sheave. [ABSTRACT FROM AUTHOR]

Let ℋq(Bn) and ℋq(Dn) denote the Hecke algebras of types Bn and Dn respectively, where q ≠ 1 is the Hecke parameter with quantum characteristic e. We prove that if Dλ is a simple ℋq(B2n)-module which splits as D + λ ⊕ D − λ upon restriction to ℋq(D2n), then D + λ ↓ ℋ q (D 2 n − 1) ≅ D − λ ↓ ℋ q (D 2 n − 1) and D + λ ↑ ℋ q (D 2 n + 1) ≅ D − λ ↑ ℋ q (D 2 n + 1) . In particular, we get some multiplicity-free results for certain two-step modular branching rules. We also show that when e = 2ℓ > 2 the highest weight crystal of the irreducible s l ^ ℓ -module L(Λ0) can be categorified using the simple ℋq (D2n)-modules { D + λ ∣ λ = (λ (1) , λ (2)) ⊢ 2 n , D λ ↓ ℋ q (D 2 n) ≅ D + λ ⊕ D − λ , n ∈ ℕ } and certain two-step induction and restriction functors. Finally, a complete classification of all the simple blocks of ℋq(Dn) is also obtained. [ABSTRACT FROM AUTHOR]

Let ℋq(Bn) and ℋq(Dn) denote the Hecke algebras of types Bn and Dn respectively, where q ≠ 1 is the Hecke parameter with quantum characteristic e. We prove that if Dλ is a simple ℋq(B2n)-module which splits as D + λ ⊕ D − λ upon restriction to ℋq(D2n), then D + λ ↓ ℋ q (D 2 n − 1) ≅ D − λ ↓ ℋ q (D 2 n − 1) and D + λ ↑ ℋ q (D 2 n + 1) ≅ D − λ ↑ ℋ q (D 2 n + 1) . In particular, we get some multiplicity-free results for certain two-step modular branching rules. We also show that when e = 2ℓ > 2 the highest weight crystal of the irreducible s l ^ ℓ -module L(Λ0) can be categorified using the simple ℋq (D2n)-modules { D + λ ∣ λ = (λ (1) , λ (2)) ⊢ 2 n , D λ ↓ ℋ q (D 2 n) ≅ D + λ ⊕ D − λ , n ∈ ℕ } and certain two-step induction and restriction functors. Finally, a complete classification of all the simple blocks of ℋq(Dn) is also obtained. [ABSTRACT FROM AUTHOR]

Classically, regular homomorphisms have been defined as a replacement for Abel-Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families of algebraically trivial cycles to abelian varieties and thereby define regular homomorphisms in the relative setting, for example, for families of schemes parameterized by a smooth variety over a given field. We establish existence and base change results, extending several results in the literature over algebraically closed fields. We also discuss the connection with intermediate Jacobians and Abel-Jacobi maps in the complex setting. [ABSTRACT FROM AUTHOR]

We study restriction of logarithmic Higgs bundles to the boundary divisor and we construct the corresponding nearby-cycles functor in positive characteristic. As applications we prove some strong semipositivity theorems for analogs of complex polarized variations of Hodge structures and their generalizations. This implies, e.g., semipositivity for the relative canonical divisor of a semistable reduction in positive characteristic and it gives some new strong results generalizing semipositivity even for complex varieties. [ABSTRACT FROM AUTHOR]

The goal of this paper is to prove the proper base change theorem for truncated coherent étale sheaves of spaces, generalizing the usual proper base change in étale cohomology. As applications, we show that the profinite étale topological type functor commutes with finite products and the symmetric powers of proper algebraic spaces over a separably closed field, respectively. In particular, the commutativity of the étale fundamental groups with finite products is extended to all higher homotopy groups. [ABSTRACT FROM AUTHOR]

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The periodic measures are investigated for a class of reaction-diffusion lattice systems driven by superlinear noise defined on Z k . The existence of periodic measures for the lattice systems is established in l 2 by Krylov-Bogolyubov's method. The idea of uniform estimates on the tails of solutions is employed to establish the tightness of a family of distribution laws of the solutions. [ABSTRACT FROM AUTHOR]

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A join-semilattice L with top is said to be conjunctive if every principal ideal is an intersection of maximal ideals. (This is equivalent to a first-order condition in the language of semilattices.) In this paper, we explore the consequences of the conjunctivity hypothesis for L, and we define and study a related property, called "ideal conjunctivity," which is applicable to join-semilattices without top. Results include the following: (a) Every conjunctive join-semilattice is isomorphic to a join-closed subbase for a compact T 1 -topology on max L , the set of maximal ideals of L, and under weak hypotheses this representation is functorial. (b) Every Wallman base for a topological space is conjunctive; we give an example of a conjunctive annular base that is not Wallman. (c) The free distributive lattice over a conjunctive join-semilattice L is a subsemilattice of the power set of max L . (d) For an arbitrary join-semilattice L: if every u-maximal ideal is prime (i.e., the complement is a filter) for every u ∈ L , then L satisfies Katriňák's distributivity axiom. (This appears to be new, though the converse is well known.) If L is conjunctive, all the 1-maximal ideals of L are prime if and only if L satisfies a weak distributivity axiom due to Varlet. We include a number of applications. [ABSTRACT FROM AUTHOR]

Let Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study ℍ(Y), a monoidal DG category that might be regarded as a categorification of the ring of differential operators on Y. When Y = LSG is the derived stack of G-local systems on a smooth projective curve, we expect ℍ(LSG) to act on both sides of the geometric Langlands correspondence, compatibly with the conjectural Langlands functor. Second, we construct a novel theory of D-modules on derived algebraic stacks. In contrast to usual D-modules, this new theory, to be denoted by Dder, is sensitive to the derived structure. Third, we identify the Drinfeld center of ℍ (Y) with Dder(LY), the DG category of Dder-modules on the loop stack LY := Y x Y x Y Y. [ABSTRACT FROM AUTHOR]

Given an ideal I on a variety X with toroidal singularities, we produce a modification X' → X, functorial for toroidal morphisms, making the ideal monomial on a toroidal stack X'. We do this by adapting the methods of [Wło05], discarding steps which become redundant. We deduce functorial resolution of singularities for varieties with logarithmic structures. This is the first step in our program to apply logarithmic desingularization to a morphism Z → B, aiming to prove functorial semistable reduction theorems. [ABSTRACT FROM AUTHOR]

The idea that gauge theory has 'surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this article, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by surplus structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any theory that represents a rich collection of physically relevant fields that are 'local' in nature. 1 Introduction 2 Theories as Categories 2.1 Relations between models 2.2 Relations between theories 3 Gauge Theory as a Category 3.1 Gauge theory on contractible manifolds 3.2 Other candidates for representing U(1) gauge theory 3.3 Surplus and inter-theoretical comparisons 4 Gauge Theory as a Functor 4.1 Richness and locality 4.2 Richness and locality imply surplus* 5 Conclusion Appendix [ABSTRACT FROM AUTHOR]

Let (R, RUS, SVR, S) be a Morita context. We study the connection between the classes of preradicals PR(R) and PR(S) of the categories of modules R-Mod and S-Mod. Two mappings between PR(R) and PR(S) are constructed from the functors HomR(U, -) and HomS(V, -). We investigate several properties of these mappings, in particular their behavior relative to the order, intersection and heredity. Similar methods were used earlier for preradicals in an adjoint situation. [ABSTRACT FROM AUTHOR]

We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathscr{D}$ -module theory following Beilinson's philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathscr{D}$ -modules whose category is equivalent to the category of overconvergent isocrystals. [ABSTRACT FROM AUTHOR]

Abstract Given a finite dimensional algebra A over an algebraically closed field, we consider the c -vectors such as defined by Fu in [18] and we give a new proof of its sign-coherence. Moreover, we characterise the modules whose dimension vectors are c -vectors as bricks respecting a functorially finiteness condition. [ABSTRACT FROM AUTHOR]

We introduce the compactness locus of a geometric functor between rigidly‐compactly generated tensor‐triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset of the tensor‐triangular spectrum of the target category which, crudely speaking, measures the failure of the functor to satisfy Grothendieck–Neeman duality (or equivalently, to admit a left adjoint). We prove that any geometric functor — even one which does not admit a left adjoint — gives rise to a Wirthmüller isomorphism once one passes to a colocalization of the target category determined by the compactness locus. When applied to the inflation functor in equivariant stable homotopy theory, this produces the Adams isomorphism. [ABSTRACT FROM AUTHOR]

Abstract Let C be an (n + 2) -angulated category with an n -suspension functor Σ n and X be a cluster-tilting subcategory of C. Then we show that the quotient category C / X is an n -abelian category, and C / X is equivalent to an n -cluster tilting subcategory of an abelian category mod (Σ − n X). In addition, if C has a Serre functor, we also prove that mod (Σ − n X) is Gorenstein of Gorenstein dimension at most n. As an application, we generalize recent results of Jacobsen-Jørgensen and Koenig-Zhu. [ABSTRACT FROM AUTHOR]

Monoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to define logical systems in order to make explicit their categorical (monoidal) structure. In this setting, logical connectives can be proven to be functors with specific properties. Accordingly, monoidal logics allow a classification of logical systems in function of their categorical structure and the functorial properties of their connectives. As they stand, however, strong parallels can be made between monoidal logics and the broader proof-theoretical framework of display logics. In this paper, we extend the results presented in Peterson ((2016). A comparison between monoidal and substructural logics. Journal of Applied Non-Classical Logics, 26(2), 126–159) and we show that monoidal logics are sound and complete with respect to associative display logics, thus providing a completeness result with regards to the algebraic semantics of display and substructural logics. In addition, we discuss the notions of classical and intuitionistic systems. Starting from Lambek's and Grishin's analyses, we explore the role played by partial De Morgan dualities and discuss the necessary and sufficient conditions required for the definitions of classical and intuitionistic deductive systems. [ABSTRACT FROM AUTHOR]

Abstract We define two model structures on the category of bicomplexes concentrated in the right half plane. The first model structure has weak equivalences detected by the totalisation functor. The second model structure's weak equivalences are detected by the E 2 -term of the spectral sequence associated to the filtration of the total complex by the horizontal degree. We then extend this result to twisted complexes. [ABSTRACT FROM AUTHOR]

For a given morphism f : X → Y in a category C having pullbacks we study some properties of the adjoint string f(-) - |f-1-1| f# and give new characterizations of monic and epic nature of the induced map f(-). [ABSTRACT FROM AUTHOR]

Abstract An algebra for a functor H is called completely iterative (cia, for short) if every flat recursive equation in it has a unique solution. Every cia is corecursive, i.e., it admits a unique coalgebra-to-algebra morphism from every coalgebra. If the converse also holds, H is called a cia functor. We prove that whenever the base category is hyper-extensive (i.e. countable coproducts are 'well-behaved') and H preserves countable coproducts, then H is a cia functor. Surprisingly few cia functors exist among standard finitary set functors: in fact, the only ones are those preserving coproducts; they are given by X ↦ W × (−) + Y for some sets W and Y. [ABSTRACT FROM AUTHOR]

Let Mfn be the localization of the ∞-category of spaces at the vn-periodic equivalences, the case n = 0 being rational homotopy theory. We prove that Mfn is for n ≥ 1 equivalent to algebras over a certain monad on the ∞-category of T(n)-local spectra. This monad is built from the Bousfield– Kuhn functor. [ABSTRACT FROM AUTHOR]

Abstract Asymptotic properties of high powers of an ideal related to a coherent functor F are investigated. It is shown that when N is an artinian module the sets of attached prime ideals Att A F (0 : N a n) are the same for n large enough. Also it is shown that for an artinian module N if the modules F (0 : N a n) have finite length and for a finitely generated module M if the modules F (M / a n M) have finite length, their lengths are given by polynomials in n , for large n. When A is local it is shown that, the Betti numbers β i (F (M / a n M)) and the Bass numbers μ i (F (M / a n M)) are given by polynomials in n for large n. [ABSTRACT FROM AUTHOR]

Abstract Let Mod- S denote the category of S -modules, where S is a small pre-additive category. Using the notion of relative derived categories of functor categories, we generalize Rickard's theorem on derived equivalences of module categories over rings to Mod- S. Several interesting applications will be provided. In particular, it will be shown that derived equivalence of two coherent rings not only implies the equivalence of their homotopy categories of projective modules, but also implies that they are Gorenstein derived equivalent. As another application, it is shown that a good tilting module produces an equivalence between the unbounded derived category of the module category of the ring and the relative derived category of the module category of the endomorphism ring of it. [ABSTRACT FROM AUTHOR]

The motive behind this paper is to generalize the concept of approach groups. In so doing, we introduce various categories, specifically, the categories of quantale-valued convergence groups, quantale-valued approach groups, quantale-valued gauge groups and quantale-valued approach system groups, and study their functorial relationships including the fact that the category of quantale-valued gauge groups as well as the category of quantale-valued approach system groups is topological over the category of groups. Besides obtaining a variety of categorical connections, we note that if the quantale is linearly ordered satisfying certain conditions, then the categories of quantale-valued approach system groups and quantale-valued gauge groups are isomorphic. Finally, we look into the embeddings of the category of quantale-valued metric groups into the categories of quantale-valued generalizations of approach groups including commutativity of some diagrams. [ABSTRACT FROM AUTHOR]

Abstract A generalized correspondence functor is a functor from the category of finite sets and T -generalized correspondences to the category of all k -modules, where T is a finite distributive lattice and k a commutative ring. We parametrize simple generalized correspondence functors using the notions of T -module and presheaf of posets. As an application, we prove finiteness and stabilization results. In particular, when k is a field, any finitely generated correspondence functor has finite length, and when k is noetherian, any subfunctor of a finitely generated functor is finitely generated. [ABSTRACT FROM AUTHOR]

Abstract We present a study on the shifted Green biset functors k R F , G of linear F -representations with coefficients over k , for fields k and F of characteristic zero and a finite group G. We provide a criterion for the vanishing of their essential algebras and we prove that the condition of uniqueness of minimal groups for simple modules holds for these functors. We give a parametrization of a family of simple k R Q , G -modules. We also prove the semisimplicity of the category of C R C , G -modules by means of an equivalence with a category of modules over a semisimple algebra. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to investigate p -stable fusion systems, where p is an odd prime. We examine realisable fusion systems and prove a generalisation of a result of G. Glauberman. Then we prove that p -stability is determined by the normaliser systems of centric radical subgroups. Finally, we prove that all p -stable fusion systems are realisable provided there exists a stable p -functor. [ABSTRACT FROM AUTHOR]

Projection algebras (spaces) can be interpreted as an algebraic version of ultrametric algebras. Computer scientists use these algebras as a convenient means for algebraic specification of process algebras. A topos-theoretic notion related to the topos PRO of projection algebras is the ideal topology which has been investigated by the authors. In this manuscript, first, we show that for any element m of the monoid ℕ∞ of extended natural numbers with the binary operation m · n = min{m, n} the notion of 'jm -separated' is the same as 'm-separated' in PRO. Then using this fact the associated sheaf functor with respect to jm is explicitly described. Furthermore, for any m ϵ ℕ∞, we provide another form of jm in terms of the implication map ↓ (m + 1) ⇒ (-) on the Heyting algebra of (right) ideals of ℕ∞. Finally, we establish a strict chain of De Morgan (sheaf) topoi in PRO. [ABSTRACT FROM AUTHOR]

Let g be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie superalgebras. The result is used in another work of the author to obtain a Jantzen sum formula for certain highest weight modules over type A Lie superalgebras. [ABSTRACT FROM AUTHOR]

By analogy with complex K –theory and K –theory with reality, there are theories of unitary functor calculus and unitary functor calculus with reality, both of which are generalisations of Weiss' orthogonal calculus. In this paper we show that unitary functor calculus can be completely recovered from the unitary functor calculus with reality, in analogy to how complex topological K –theory is completely recovered from K –theory with reality via forgetting the C 2 –action. [ABSTRACT FROM AUTHOR]

Abstract Let G be the F -points of a connected reductive group over a non-archimedean local field F of residue characteristic p and R be a commutative ring. Let P = L U be a parabolic subgroup of G and Q be a parabolic subgroup of G containing P. We study the functor St Q G taking a smooth R -representation σ of L which extends to a representation e G (σ) of G trivial on U to the smooth R -representation e G (σ) ⊗ R St Q G (R) of G where St Q G (R) is the generalised Steinberg representation. [ABSTRACT FROM AUTHOR]

Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a pair: bicategory and endobifunctor . For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the endofunctor Σq such that Σqα:=q-degαΣα for any 2-morphism α and coincides with Σ otherwise. Applying the quantized trace to the bicategory of Chen-Khovanov bimodules we get a new triply graded link homology theory called quantum annular link homology. If q=1 we reproduce Asaeda-Przytycki-Sikora homology for links in a thickened annulus. We prove that our homology carries an action of , which intertwines the action of cobordisms. In particular, the quantum annular homology of an n-cable admits an action of the braid group, which commutes with the quantum group action and factors through the Jones skein relation. This produces a nontrivial invariant for surfaces knotted in four dimensions. Moreover, a direct computation for torus links shows that the rank of quantum annular homology groups depend on the quantum parameter q. [ABSTRACT FROM AUTHOR]

Abstract In order to enable experimentations and simulations of bigraphs, we need an implementation of their dynamics. In this paper, we tackle the matching issue of this task. We present a solution based on an investigation on graph matching. We propose to simulate a bigraphical reactive system (i.e., bigraphs with a set of reaction rules that allow their rewriting) with a graph transformation system. First, we translate a bigraph to a ranked graph. This translation is ensured by defining a faithful functor that allows to move from the bigraph category to the ranked graph category. Then, we show that reaction rules can be simulated with graph rules. Hence, we provide a formal basis allowing to execute bigraph transformations by simulating their translation aiming to use well-established and efficient graph transformation tools. [ABSTRACT FROM AUTHOR]

We give an abstract characterization of the category of co-semi-analytic functors and describe an action of semi-analytic functors on co-semi-analytic functors. [ABSTRACT FROM AUTHOR]

We construct a covariant functor γ from the category of monadic MV-algebras into the category of Q-distributive lattices, i.e., distributive lattices with quantifier introduced by R. Cignoli. For every monadic MV-algebra, we construct a dual object named QM-space; these objects form a special subcategory of spectral spaces and of Q-spaces developed by R. Cignoli for Q-distributive lattices. [ABSTRACT FROM AUTHOR]