Let X be an elliptic curve over an algebraically closed field. We prove that some exact sub-categories of the category of vector bundles over X, defined using Harder-Narasimhan filtrations, have the same K-groups as the whole category.

1.1. Definition. Let C be an abelian category. The derivative D(C) of C is defined as follows: The objects are exact sequences 0 −→ X0 iX −−→ X1 πX −−→ X0 −→ 0 of C, and the morphisms from such an object are morphisms of exact sequences whose two X parts coincide. The category D(C) is again abelian. An exact functor F : C1 −→ C2 gives rise to an induced (exact) functor D(F ) : D(C1) −→ D(C2). W...

In this paper, we study the notion of Cauchy-complete preorder in a regular category, following work in [CS86], introducing the logic of a regular category. We give a different, stronger characterization than in loc.cit. for those preorders. Using this, we provide a new construction of the Cauchy-completion in a exact category. AMS Classification: 18A40, 03G30.

In this study, we first define the concept of inverse and direct system in category of fuzzy modules. We investigate whether or not limit of inverse (direct) system of exact sequences of fuzzy modules is exact. Later, we show that direct system limit of exact sequences of fuzzy modules is exact. Generally, limit of inverse system of exact sequences is not exact. Then we define the notion ← (1) ...

In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

We fill a gap in the literature regarding ‘transport of structure’ for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing (classical higher) homological algebra. As an application our main results, we show that skeleton one these kinds inherits same structure canonical way, up to equivalence. In particular, it follows weak (n+2)-angulated category is fact what call stron...

A new description of the exact completion Cex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under finite limits and coequalizers of equivalence relations. An infinitary generalization is proved, and the classical description of the exact completion is derived.

A new description of the exact completion C ex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under nite limits and coequalizers of equivalence relations. An innnitary generalization is proved, and the classical description of the exact completion is derived.