Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
Exact $(\infty,1)$-categories are the analog in (∞,1)-category theory of exact categories in category theory.
Let $\mathcal{C}$ be an (∞,1)-category. This is called an exact $(\infty,1)$-category if
$\mathcal{C}$ has a terminal object and (∞,1)-fiber products;
groupoid objects in $\mathcal{C}$ are effective:
realization of groupoid objects is universal.
There is another meaning for “exact (∞,1)-category” for which there is a Quillen Q-construction for exact (∞,1)-categories which allows to compute its algebraic K-theory.
regular (infinity,1)-category, coherent (infinity,1)-category?, (infinity,1)-pretopos
On exact $\infty$-categories
and the theorem of the heart:
Last revised on July 7, 2023 at 18:13:49. See the history of this page for a list of all contributions to it.