nLab
semiadditive (∞,1)-category

Contents

Context

Additive and abelian categories

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

Limits and colimits

Contents

Idea

An (∞,1)-category is nn-semiadditive for nn \in \mathbb{N} if (∞,1)-colimits over certain diagrams coincide with their (∞,1)-limits in a canonical way (see Hopkins-Lurie 14, def. 4.4.2). Here for n=0n=0 the condition is that coproducts coincide with products, hence that bilimits exist.

So an (∞,1)-category that happens to be an ordinary category is 0-semiadditive precisely if it is a semiadditive category in the traditional sense. Generally, an (∞,1)-category is 0-semiadditive precisely if its homotopy category is semiadditive (Hopkins-Lurie 14, remark 4.4.13).

Examples

References

Last revised on February 2, 2014 at 05:40:32. See the history of this page for a list of all contributions to it.