nLab
exact (infinity,1)-category

Contents

Contents

Idea

An exact (,1)(\infty,1)-category is the analog of an exact category for (∞,1)-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 homotopy 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

References for the version of exactness suitable for the Q construction

Last revised on June 12, 2021 at 05:57:18. See the history of this page for a list of all contributions to it.