On the notion of precohomology
On the Spectral Category of Some Rings.
On three types of simplicial objects
Polytopal linear algebra.
Preserving homology.
Quelques remarques sur les opérateurs et les q-algèbres de Banach.
Quotient Banach spaces
Quotient Banach spaces; Multilinear theory
Quotients, fractions, symmetrizations
Realization of long exact sequences of abelian groups.
Given a long exact sequence of abelian groupsL: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories...
Relative EXT groups of Abelian categories
Relative theory in subcategories
We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].
Semi-abelian monadic categories.
Semilocalizations of exact and leftextensive categories
Sous-quotients et relations induites dans les catégories exactes
Stable short exact sequences and the maximal exact structure of an additive category
It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.
Subspaces in abstract Stone duality.
Sur les quasi-limites
The category of long exact sequences and the homotopy exact sequence of modules.
The homotopy category of chain complexes is a homotopy category