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Abstract We establish the universal properties of the bicategory of polynomials, considering both cartesian and general morphisms between these polynomials. A direct proof of these universal properties would be impractical due to the complicated coherence conditions arising from polynomial composition; however, in this paper we avoid most of these coherence conditions using the properties of generic bicategories. In addition, we give a new proof of the universal properties of the bicategory of spans, and also establish the universal properties of the bicategory of spans with invertible 2-cells; showing how these properties may be used to describe the universal properties of polynomials. [ABSTRACT FROM AUTHOR]

Let (R,m) be a d-dimensional commutative Noetherian local ring. Let M denote themorphism category of finitely generated R-modules, and let S be the full subcategory ofMconsisting of monomorphisms, known as the submodule category. This article reveals that the Auslander transpose in the category S can be described explicitly withinmodR, the category of finitely generated R-modules. This result is exploited to study the linkage theory as well as the Auslander-Reiten theory in S. In addition, motivated by a result of Ringel and Schmidmeier, we show that the Auslander-Reiten translations in the subcategories H and G, consisting of all morphisms which are maximal Cohen-Macaulay R-modules and Gorenstein projective morphisms, respectively, may be computed within modR via G-covers. The corresponding result for the subcategory of epimorphisms in H is also obtained. [ABSTRACT FROM AUTHOR]

In this essay, we study various notions of projective space (and other schemes) over F1ℓ, with F1 denoting the field with one element. Our leading motivation is the "Hidden Points Principle," which shows a huge deviation between the set of rational points as closed points defined over F1ℓ and the set of rational points defined as morphisms 𝚂𝚙𝚎𝚌(F1ℓ)↦X. We also introduce, in the same vein as Kurokawa [Proc. Jpn. Acad. Ser. A Math. Sci. 81 (2005), pp. 180–184], schemes of F1ℓ‐type and consider their zeta functions. [ABSTRACT FROM AUTHOR]

Given a morphism F:X→Y from a Mori Dream Space X to a smooth Mori Dream Space Y and quasicoherent sheaves F on X and G on Y, we describe the inverse image of G by F and the direct image of F by F in terms of the corresponding modules over the Cox rings graded in the class groups. [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]

By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib(B) of fibrations with a fixed base category B and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations Fib→Cat. [ABSTRACT FROM AUTHOR]

We give a functorial description of the Kato–Nakayama space of a fine saturated log analytic space, that is similar in spirit to the functorial description of root stacks. As a consequence we get a global description of the comparison map constructed in [ 2 ] from the Kato–Nakayama space to the (topological) infinite root stack. [ABSTRACT FROM AUTHOR]

In [17], the first author introduced (relative) Riemann-Zariski spaces corresponding to a morphism of schemes and established their basic properties. In this article, we clarify that theory and extend it to morphisms between algebraic spaces. As an application, a new proof of Nagata's compactification theorem for algebraic spaces is obtained. [ABSTRACT FROM AUTHOR]

Let R be a ring. An additive mapping f : R ≤ R is called 3-homomorphism (resp. 3-antihomomorphsm) on R if f(xyz) = f(x)f(y)f(z) (resp. f(xyz) = f(z)f(y) f(x)) for all x, y, z ∊ R. In the present paper, we characterize multiplicative (generalized)- derivation which acts as a 3-homomorphism or as a 3-antihomorphism on an appropriate subset of a ring R. [ABSTRACT FROM AUTHOR]

We fix any bicategory A together with a class of morphisms W A , such that there is a bicategory of fractions A [ W A − 1 ] (as described by D. Pronk). Given another such pair ( B , W B ) and any pseudofunctor F : A → B , we find necessary and sufficient conditions in order to have an induced pseudofunctor G : A [ W A − 1 ] → B [ W B − 1 ] . Moreover, we give a simple description of G in the case when the class W B is “right saturated”. [ABSTRACT FROM AUTHOR]

In this paper, firstly we recall some definitions and basic properties of soft set theory, category theory and soft category theory. We study on soft monomorphism, soft epimorphism, equalizer and coequalizer for soft categories. We gave some properties of these soft morphisms. We proved that the soft Category SFun has coequalizers, equalizer of a morphism pair in SFun category is soft monic and coequalizers of a morphism pair in SFun category is soft epic. [ABSTRACT FROM AUTHOR]

An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular . Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional local rings. [ABSTRACT FROM AUTHOR]

The purpose in this paper is to prove the existence of a canonical-pre-quasi-uniform extension ( X , U ) ˆ of a pre-quasi-uniform space ( X , U ) . Most of the concepts used in quasi-uniform spaces may be applied to pre-quasi-uniform spaces. These spaces were introduced by the first author and developed by the second in his doctoral thesis. We shall study the main properties of this class of spaces which contains the class of quasi-uniform spaces. [ABSTRACT FROM AUTHOR]

In this paper we describe a package for which constructs crossed modules of k-algebras and cat1-algebras over k, and their morphisms. We include a table of cat1-algebras. [ABSTRACT FROM AUTHOR]

The concepts of relative growth indicators such as relative order, relative type, relative weak type, etc. have widely been used to avoid comparing growths of entire and meromorphic functions just with exp functions. Using the notions of several relative growth indicators as mentioned earlier, in this paper we would like to find out the limits in terms of classical growth indicators (i.e. order, type, weak type etc.) in which the relative type, relative weak type, etc. of meromorphic functions with respect to entire functions should lie. [ABSTRACT FROM AUTHOR]

Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the theory of "gleaves", which are presheaves equipped with an additional "gluing operation" of compatible pairs of local sections. This generalizes the conditional product structures of Dawid and Studeny, which correspond to gleaves on distributive lattices. Our examples include the gleaf of metric spaces and the gleaf of joint probability distributions. A result of Johnstone shows that a category of gleaves can have a subobject classifier despite not being cartesian closed. Gleaves over the simplex category Δ, which we call compositories, can be interpreted as a new kind of higher category in which the composition of an m-morphism and an n-morphism along a common κ-morphism face results in an (m + n -- k)-morphism. The distinctive feature of this composition operation is that the original morphisms can be recovered from the composite morphism as initial and final faces. Examples of compositories include nerves of categories and compositories of higher spans. [ABSTRACT FROM AUTHOR]

Let (W, q, D) be a 4-dimensional Walker manifold. After providing a characterization and some examples for several special (1, 1)-tensor fields on (W, q, D), we prove that the proper almost complex structure J, introduced by Matsushita, is harmonic in the sense of García-Río et al. if and only if the almost Hermitian structure (J, q) is almost Kähler. We classify all harmonic functions locally defined on (W, q, D) . We deal with the harmonicity of quadratic maps defined on ℝ4 (endowed with a Walker metric q) to the n-dimensional semi-Euclidean space of index r, and then between local charts of two 4-dimensional Walker manifolds. We obtain here the necessary and sufficient conditions under which these maps are harmonic, horizontally weakly conformal, or harmonic morphisms with respect to q. [ABSTRACT FROM AUTHOR]

In this paper we construct a new morphism of matrix coalgebras, than we prove that it is an epimorphism and also that its kernel is a coideal in the matrix coalgebra. Finally we give a generalization on this type of morphism between two matrix coalgebras. [ABSTRACT FROM AUTHOR]

The classical snake lemma produces a six terms exact sequence starting from a commutative square with one of the edge being a regular epimorphism. We establish a new diagram lemma, that we call snail lemma, removing such a condition. We also show that the snail lemma subsumes the snake lemma and we give an interpretation of the snail lemma in terms of strong homotopy kernels. Our results hold in any pointed regular protomodular category. [ABSTRACT FROM AUTHOR]

We show that the morphism axiom for n-angulated categories is redun- dant. [ABSTRACT FROM AUTHOR]

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective covers and we interpret these constructions in terms of adjoint functors. [ABSTRACT FROM AUTHOR]

The well-known embedding of full intuitionistic propositional calculus into the atomic polymorphic system Fat is possible due to the intriguing phenomenon of instantiation overflow. Instantiation overflow ensures that (in Fat) we can instantiate certain universal formulas by any formula of the system, not necessarily atomic. Until now only three types in Fat were identified with such property: the types that result from the Prawitz translation of the propositional connectives (⟘,Λ,∨) into Fat (or Girard's system F). Are there other types in Fat with instantiation overflow? In this paper we show that the answer is yes and we isolate a class of formulas with such property. [ABSTRACT FROM AUTHOR]

Algebraic weak factorisation systems ( awfs ) refine weak factorisation systems by requiring that the assignations sending a map to its first and second factors should underlie an interacting comonad–monad pair on the arrow category. We provide a comprehensive treatment of the basic theory of awfs —drawing on work of previous authors—and complete the theory with two main new results. The first provides a characterisation of awfs and their morphisms in terms of their double categories of left or right maps. The second concerns a notion of cofibrant generation of an awfs by a small double category; it states that, over a locally presentable base, any small double category cofibrantly generates an awfs , and that the awfs so arising are precisely those with accessible monad and comonad. Besides the general theory, numerous applications of awfs are developed, emphasising particularly those aspects which go beyond the non-algebraic situation. [ABSTRACT FROM AUTHOR]

We introduce a notion of bimodule in the setting of enriched ∞-categories, and use this to construct a double ∞-category of enriched ∞-categories where the two kinds of 1-morphisms are functors and bimodules. We then consider a natural definition of natural transformations in this context, and show that in the underlying (∞, 2)-category of enriched ∞-categories with functors as 1-morphisms the 2-morphisms are given by natural transformations. [ABSTRACT FROM AUTHOR]

It is shown that the ring of fractions of the algebra of all bounded linear operators on a separable infinite dimensional Banach space is isomorphic to the Adams completion of the algebra with respect to a carefully chosen set of morphisms in the category of separable infinite dimensional Banach spaces and bounded linear norm preserving operators of norms at most 1. [ABSTRACT FROM AUTHOR]

In this article we consider moduli properties of singular curves on K3 surfaces. Let B g denote the stack of primitively polarized K3 surfaces ( X , L ) of genus g and let T g , k n → B g be the stack parameterizing tuples [ ( f : C → X , L ) ] with f an unramified morphism which is birational onto its image, C a smooth curve of genus p ( g , k ) − n and f ⁎ C ∈ | k L | . We show that the forgetful morphism η : T g , k n → M p ( g , k ) − n is generically finite on at least one component, for all but finitely many values of p ( g , k ) − n . We further study the Brill–Noether theory of those curves parametrized by the image of η , and find a Wahl-type obstruction for a smooth curve with an unordered marking to have a nodal model on a K3 surface in such a way that the marking is the divisor over the nodes. [ABSTRACT FROM AUTHOR]

The Dual Post Correspondence Problem asks, for a given word α , if there exists a non-periodic morphism g and an arbitrary morphism h such that g ( α ) = h ( α ) . Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing , and are important to the study of word equations, equality sets and ambiguity of morphisms. In this paper, a ‘prime’ subset of periodicity forcing words is presented. It is shown that when combined with a particular type of morphism it generates exactly the full set of periodicity forcing words. Furthermore, it is shown that there exist examples of periodicity forcing words which contain any given factor/prefix/suffix. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already. [ABSTRACT FROM AUTHOR]

We study problems inspired by language theory in certain matrix monoids which are extensions of free monoids. In particular, we characterize free two-element sets, morphisms and morphic equality sets in these monoids. [ABSTRACT FROM AUTHOR]

Let A and B be Banach algebras and T: B → A be a continuous homomorphism. n-weak amenability of the Banach algebra A × T B (defined in Bade, W. G., Curtis, P. C., Dales, H. G.: Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55(2), 359-377 (1987)) is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied. [ABSTRACT FROM AUTHOR]

Let G be a connected reductive group with connected center defined over Fq, with Frobenius morphism F. We parameterize all of the real-valued irreducible complex characters of GF using the Jordan decomposition of characters. [ABSTRACT FROM AUTHOR]

We develop various properties of étale Borel–Moore homology and study its relationship with intersection theory. Using Gabber's localized cycle classes we define étale homological Gysin morphisms and show that they are compatible with the cycle class map and Gysin morphisms in intersection theory. We also study étale versions of bivariant operations, and establish their compatibility with Riemann–Roch transformations and Fulton–MacPherson bivariant operations. As an application of these techniques we show that in certain situations local terms for correspondences acting on étale cohomology are given by cycle classes. [ABSTRACT FROM AUTHOR]

Letbe a Leibniz algebra,be a vector space andbe an epimorphism of vector spaces with. The global extension problem asks for the classification of all Leibniz algebra structures that can be defined onsuch thatis a morphism of Leibniz algebras: from a geometrical viewpoint this is to give the decomposition of the groupoid of all such structures in its connected components and to indicate a point in each component. All such Leibniz algebra structures onare classified by a global cohomological objectwhich is explicitly constructed. It is shown thatis the coproduct of all local cohomological objectswhich are classifying sets for all extensions ofby all Leibniz algebra structureson. The second cohomology groupof Loday and Pirashvili appears as the most elementary piece among all components of. Several examples are worked out in details for co-flag Leibniz algebras over, i.e. Leibniz algebrasthat have a finite chain of epimorphisms of Leibniz algebrassuch that, for all. Metabelian Leibniz algebras are introduced, described and classified using pure linear algebra tools. [ABSTRACT FROM AUTHOR]

Let ( X , B ) be a complex projective klt pair, and let f : X → Z be a surjective morphism onto a normal projective variety with maximal albanese dimension such that K X + B is relatively big over Z . We show that such pairs have good log minimal models. [ABSTRACT FROM AUTHOR]

In this paper, we provide some formulae to calculate orbital characters. Especially we give a lifting theorem by which one can read off the value of orbital characters from local subgroups. With orbital characters, we can show that Reynolds ideal is dual to the vector space of simple modules and this leads to a new method to count simple modules. We also give a natural morphism from local to general vector space of simple modules and determine it completely. Some other applications to modular representation are also included. [ABSTRACT FROM AUTHOR]

We prove that if we considerto be an unbranched Riemann domain between two complex spaces with isolated singularities,is-complete andis a Stein morphism, thenis-complete. [ABSTRACT FROM PUBLISHER]

We show that injectives with respect to a specific class of order embeddings in the category of posemigroups with submultiplicative morphisms are quantales and construct injective hulls for a certain class of posemigroups with respect to this specific class of order embeddings. [ABSTRACT FROM AUTHOR]

Let f: Ω → f(Ω) ⊂ ℝ be a W-homeomorphism with L-integrable inner distortion. We show that finiteness of min{lip ( x), k ( x)}, for every x ∈ Ω\ E, implies that f ∈ W and has finite distortion, provided that the exceptional set E has σ-finite ℋ-measure. Moreover, f has finite distortion, differentiable a.e. and the Jacobian J > 0 a.e. [ABSTRACT FROM AUTHOR]

A circle action $S^{1}\times M\rightarrow M$ on a manifold $M$ is called regular if this action is free and the orbit space is a manifold. In this paper, we determine the homeomorphism (respectively, diffeomorphism) types of those 2-connected 7-manifolds (respectively, smooth 2-connected 7-manifolds) that admit regular circle actions (respectively, smooth regular circle actions). [ABSTRACT FROM PUBLISHER]

Abstract: Consider an exact couple in a semiabelian category in the sense of Palamodov, i.e., in an additive category in which every morphism has a kernel as well as a cokernel and the induced morphism between coimage and image is always monic and epic. Assume that the morphisms in the couple are strict, i.e., they induce even isomorphisms between their corresponding coimages and images. We show that the classical construction of Eckmann and Hilton in this case produces two derived couples which are connected by a natural bimorphism. The two couples correspond to the a priori distinct cohomology objects, the left resp. right cohomology, associated with the initial exact couple. The derivation process can be iterated under additional assumptions. [Copyright &y& Elsevier]

Abstract: We give the complete classification of -bundles over projective manifolds of Picard number one each of which admit another smooth morphism of relative dimension one. [Copyright &y& Elsevier]

It is a well-known result of the covering groups that a subgroup G of the fundamental group at the identity of a semilocally simply connected topological group determines a covering morphism of topological groups with characteristic group G. In this paper we generalize this result to a large class of algebraic objects called topological groups with operations, including topological groups. We also prove that the crossed modules and internal categories within topological groups with operations are equivalent. This equivalence enables us to introduce the cover of crossed modules within topological groups with operations. Finally, we draw relations between the coverings of an internal groupoid within topological groups with operations and those of the corresponding crossed module. [ABSTRACT FROM AUTHOR]

We extend the classical Schwarz Lemma to homeomorphisms with integrally bounded p-module in ℝ n. [ABSTRACT FROM AUTHOR]

Abstract: We introduce the notions of preordered and heap-preordered forests, generalizing the construction of ordered and heap-ordered forests. We prove that the algebras of preordered and heap-preordered forests are Hopf for the cut coproduct, and we construct a Hopf morphism to the Hopf algebra of packed words. Moreover, we define another coproduct on the preordered forests given by the contraction of edges. Finally, we give a combinatorial description of morphism defined on Hopf algebras of forests with values in the Hopf algebras of shuffles or quasi-shuffles. [Copyright &y& Elsevier]

For irreducible rational representations of the classical algebraic groups in characteristic p > 2, which are not equivalent to the composition of a group morphism and the standard representation, it is proved that usually the image of a unipotent element of order p > p has at least two Jordan blocks of size > p; all exceptions are indicated explicitly. As a corollary, irreducible rational representations of these groups whose images contain unipotent elements with just one Jordan block of size > 1 are classified. [ABSTRACT FROM AUTHOR]

For a certain class of groups under a given finite group F, we define and compute genus groups, which coincide with the known genus groups in the case that F is the trivial group. We prove the existence of various induced homomorphisms between genus groups. We discover an induced morphism arising from factoring out a finite normal subgroup. [ABSTRACT FROM AUTHOR]

We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal'tsev varieties. [ABSTRACT FROM AUTHOR]

In this paper first we define the morphism between geometric spaces in two different types. We construct two categories of U- GESP and L- GESP from geometric spaces then investigate some properties of the two categories, for instance U- GESP is topological. The relation between hypergroups and geometric spaces is studied. By constructing the category SNS- Hv of Hv- groups we answer the question that which construction of hyper- structures on the category of sets has free object in the sense of universal property. At the end we define the category of geometric hypergroups and we study its relation with the category of hyper- group. [ABSTRACT FROM AUTHOR]

Abstract: A generalized pseudostandard word u, as introduced in 2006 by de Luca and De Luca, is given by a directive sequence of letters from an alphabet and by a directive sequence of involutory antimorphisms acting on . Prefixes of u with increasing length are constructed using a pseudopalindromic closure operator. We show that generalized Thue–Morse words , with and b, , are generalized pseudostandard words if and only if is a periodic word or . This extends the result of de Luca and De Luca obtained for the classical Thue–Morse words. [Copyright &y& Elsevier]