Fully bounded grothendieck categories part II: Graded modules

Triangulated Categories Part II

The results in this note are all from [Nee01] or [BN93]. For necessary background on cardinals (particularly regular and singular cardinals) see our notes on Basic Set Theory (BST). In our BST notes there is no mention of grothendieck universes, whereas all our notes on category theory (including this one) are implicitly working inside a fixed grothendieck universe U using the conglomerate conv...

Derived Categories Part II

2 Derived Functors 2 2.1 Classical Derived Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Localisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Bounded Derived Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Linear Derived Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

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 ...

Grothendieck Categories and Support Conditions

Grothendieck Categories and Support Conditions