additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
If is a commutative ring, -linear (infinity,1)-categories are the analogue in (∞,1)-category theory of the notion of -linear category in category theory.
A -linear (infinity,1)-category is an additive (infinity,1)-category whose homotopy category is a -linear category.
More generally, let be a commutative ring spectrum and let denote the symmetric monoidal (infinity,1)-category of modules over it. An -linear (infinity,1)-category is an object of the (infinity,1)-category of modules over in the symmetric monoidal (infinity,1)-category of (infinity,1)-categories.
An -linear (infinity,1)-category is naturally enriched over the symmetric monoidal (infinity,1)-category of modules over .
Section 6 of
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