Objets quasi-injectifs dans une catégorie abélienne avec générateur et limites inductives exactes
On -exact categories
An -exact category is a pair consisting of an additive category and a class of sequences with terms satisfying certain axioms. We introduce -weakly idempotent complete categories. Then we prove that an additive -weakly idempotent complete category together with the class of all contractible sequences with terms is an -exact category. Some properties of the class are also discussed.
On n-permutable equivalence relations in regular categories
On reflective subcategories of quasiabelian categories.
On the categorical foundations of homological and homotopical algebra
On the characterization of Jonsson-Tarski and of subtractive varieties
On the characterization of monadic categories over set
On the cohomology sequence in a semiabelian category.
On the Freyd categories of an additive category.
On the maximal exact structure of an additive category
We prove that every additive category has a unique maximal exact structure in the sense of Quillen.
On the notion of precohomology
On the Spectral Category of Some Rings.
On three types of simplicial objects
One-sided -suspended categories
For an integer , we introduce a simultaneous generalization of -exact categories and -angulated categories, referred to as one-sided -suspended categories. Notably, one-sided -angulated categories are specific instances of this structure. We establish a framework for transitioning from these generalized categories to their -angulated counterparts. Additionally, we present a method for constructing -angulated quotient categories from Frobenius -prile categories. Our results unify and extend...