Exactly Definable Categories

Definable Additive Categories

This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2-category which

Abelian categories and definable additive categories

2 The category of small abelian categories and exact functors 4 2.1 Categorical properties of ABEX . . . . . . . . . . . . . . . . . . . 5 2.2 Pullbacks in ABEX . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 ABEX is finitely accessible . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Abelian categories as schemes . . . . . . . . . . . . . . . . . . . . 16 2.4.1 The functor of point...

Categories of imaginaries for definable additive categories

An additive category is definable if it is equivalent to a definable subcategory of a module category Mod-R, meaning a full subcategory which is closed under direct products, direct limits (= directed colimits) and pure subobjects. Such a category D has associated to it a canonical model theory for its objects in the sense that each object D ∈ D becomes a structure for the associated language; ...

Definable additive categories: purity and model theory

Structure sheaves of definable additive categories