additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
equivalences in/of $(\infty,1)$-categories
An (∞,1)-category is $n$-semiadditive for $n \in \mathbb{N}$ 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 $n=0$ 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).
Last revised on February 2, 2014 at 05:40:32. See the history of this page for a list of all contributions to it.