nLab exact (infinity,1)-category

Redirected from "exact (∞,1)-categories".
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Contents

Idea

Exact (,1)(\infty,1)-categories are the analog in (∞,1)-category theory of exact categories in category theory.

Definition

Definition

Let 𝒞\mathcal{C} be an (∞,1)-category. This is called an exact (,1)(\infty,1)-category if

  1. 𝒞\mathcal{C} has a terminal object and (∞,1)-fiber products;

  2. groupoid objects in 𝒞\mathcal{C} are effective:

  3. realization of groupoid objects is universal.

Other notions of “exact”

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.

References

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.