We investigate abelian quotients arising from extriangulated categories via morphism categories, which is a unified treatment for both exact and triangulated categories. Let $(\mathcal {C},\mathbb {E},\mathfrak {s})$ be an category with enough projectives $\mathcal {P}$ ${\mathscr{M}}$ full subcategory of {C}$ containing . show that certain quotient $\mathfrak {s}\textup {-def}({\mathscr{M}})$ ...

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

We investigated maximal Prym varieties on finite fields by attaining their upper bounds on the number of rational points. This concept gave us a motivation for defining a generalized definition of maximal curves i.e. maximal morphisms. By MAGMA, we give some non-trivial examples of maximal morphisms that results in non-trivial examples of maximal Prym varieties.

Harmonic morphism is a smooth map between Riemannian manifolds which pulls back germs of harmonic functions to germs of harmonic functions. It may be charactrized as harmonic maps which are horizontally weakly conformal [5,9]. One task of studying harmonic morphism is constructing concrete examples; Another one is classification of all harmonic morphisms between all special manifolds (in partic...

A factorization of a Galois connection investigated earlier is used to give a definition of a connectedness-disconnectedness Galois connection that is free of the notion of constant morphism. A new notion of N -fixed morphism with respect to a classN of monomorphisms is presented. This is used to characterize the connectedness-disconnectedness Galois connection in the case that N is closed unde...

This paper gives a description of all harmonic morphisms from a threedimensional non-simply-connected Euclidean and spherical space form to a surface, by extending the work of Baird-Wood [4, 5] who dealt with the simply-connected case; namely we show that any such harmonic morphism is the composition of a “standard” harmonic morphism and a weakly conformal map. To complete the description we li...

We describe the relationship between different parameters of the initial word and its image obtained by application of a uniform marked morphism. The functions described include the subword complexity, frequency of factors, and the recurrence function. The relations obtained for the image of a word can be used also for the image of a factorial language. Using induction, we give a full descripti...

the category whose objects aremorphisms of fine saturated log schemes Y log → X , where Y is a noetherian scheme, and the underlying morphism of schemes Y → X is of finite type, and whose morphisms (from an object Y log 1 → X log to an object Y log 2 → X ) are morphisms of finite type Y log 1 → Y log 2 (i.e., morphisms for which the underlying morphism of schemes Y1 → Y2 is of finite type) lyin...