# nLab sifted (infinity,1)-colimit

### Context

#### Limits and colimits

limits and colimits

# Contents

## Definition

A sifted $(\infty,1)$-colimit is an (∞,1)-colimit over a diagram that is a sifted (∞,1)-category.

## Properties

###### Proposition

Let $C$ be an (∞,1)-category such that products preserve sifted (∞,1)-colimits (for instance an (∞,1)-topos, see universal colimits).

Then sifted (∞,1)-colimits preserve finite products.

This is (Lurie, lemma 5.5.8.11).

• sifted colimit, sifted $(\infty,1)$-colimit

## References

Last revised on August 25, 2017 at 01:36:00. See the history of this page for a list of all contributions to it.