Contents

# Contents

## Idea

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

## Definition

###### Definition

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

1. $\mathcal{C}$ has a terminal object and homotopy fiber products;

2. groupoid objects in $\mathcal{C}$ 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.