An exact $(\infty,1)$-category is the analog of an exact category for (∞,1)-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 homotopy 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
References for the version of exactness suitable for the Q construction
Clark Barwick, On the Q construction for exact quasicategories (arXiv:1301.4725)
Clark Barwick, On exact infinity-categories and the Theorem of the Heart (arXiv:1212.5232)
Last revised on June 12, 2021 at 05:57:18. See the history of this page for a list of all contributions to it.