Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

The category of simplicial ℛ–coalgebras over a presheaf of commutative unital rings on a
small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

This paper is a commutative algebra introduction to the homological theory of quasi-
coherent sheaves and contraherent cosheaves over quasi-compact semi-separated …

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …

Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …

We investigate adjoint and Frobenius pairs between categories of comodules over rather
general corings. We particularize to the case of the adjoint pair of functors associated to a …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

In this paper we prove the existence of a flat cover and a cotorsion envelope for any quasi-
coherent sheaf over the projective line, where R is any commutative ring. We first prove a …