Exactness of the double dual and Morita duality for grothendieck categories

Semi-abelian Categories and Exactness

We show that every semi-abelian category, as defined by Palamodov, possesses a maximal exact structure in the sense of Quillen and that the exact structure of a quasi-abelian category is a special case thereof.

Grothendieck Categories and Support Conditions

Non-noetherian Grothendieck Duality

For any separated map f : X → Y of quasi-compact quasiseparated schemes, Rf∗ : D + qc(X) → D (Y ) has a right adjoint f . If f is proper and pseudo-coherent (e.g., finitely-presented and flat) then Duality and tor-independent Base Change hold for f . Preface This is a research summary written early in 1991, concerning results obtained by the author during a stay at MSRI in Berkeley during 1989–...

Grothendieck Categories and Support Conditions

Atomical Grothendieck Categories

Motivated by the study of Gabriel dimension of a Grothendieck category, we introduce the concept of atomical Grothendieck category, which has only two localizing subcategories, and we give a classification of this type of Grothendieck categories. 1. Introduction. Given a Grothendieck category Ꮽ, we can associate with it the lattice of all localizing categories of Ꮽ and denote it by Tors(Ꮽ). We ...