Homological Functor H n: Comp(π) βΆ Ab Where π Is an Abelian Category and π Is an Integer in β€
Year: 2025
Type: article
Abstract: The study of the homological functor has been carried out in particular cases of abelian categories, notably in the category of left A-modules (resp. right A-modules) and Categories of graded A-modules where A is a ring. We call category of complexes of an abelian category π the category denoted by Comp(π) whose objects are the complexe sequence of π and morphisms are the chain maps of π. In this paper, we consider the functor HΜn define by the composition of functors Hn β HomComp(π)(X,-), where HomComp(π)(X,-) is define by Comp(π) β Comp(Ab), the functor Hn is define by Comp(Ab) β Ab and X is a projective object of π. In this article, we study how the homological functor HΜn define by Comp(π) βΆ Ab where π is an abelian category and π is an integer in β€ transforms a short exact sequence into a long exact sequence. The main results of this paper are: the construction of the connecting morphism Οn associated to the covariant functor HΜn, and show that HΜn transforms all short exact sequence of morphisms in Comp(π) into a long exact sequence of morphisms in Ab, where X is an projectif object in π and π is an abelian category.
Author: Ablaye Diallo
Institution: UniversitΓ© Gaston Berger
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417226104