nLab
linear (∞,1)-category

Context

Additive and abelian categories

(,1)(\infty,1)-Category theory

Contents

Idea

If kk is a commutative ring, kk-linear (infinity,1)-categories are the analogue in (∞,1)-category theory of the notion of kk-linear category in category theory.

Definition

A kk-linear (infinity,1)-category is an additive (infinity,1)-category AA whose homotopy category ho(A)ho(A) is a kk-linear category.

More generally, let RR be a commutative ring spectrum and let Mod(R)Mod(R) denote the symmetric monoidal (infinity,1)-category of modules over it. An RR-linear (infinity,1)-category is an object of the (infinity,1)-category of modules over Mod(R)Mod(R) in the symmetric monoidal (infinity,1)-category of (infinity,1)-categories.

Properties

An RR-linear (infinity,1)-category is naturally enriched over the symmetric monoidal (infinity,1)-category of modules over RR.

References

Section 6 of

Last revised on January 25, 2015 at 15:55:43. See the history of this page for a list of all contributions to it.