# nLab sifted colimit

### Context

#### Limits and colimits

limits and colimits

# Contents

## Definition

A sifted colimit is a colimit of a diagram $D\to C$ where $D$ is a sifted category (in analogy with a filtered colimit, involving diagrams of shape a filtered category). Such colimits commute with finite products in Set by definition.

## Examples

A motivating example is a reflexive coequalizer. In fact, sifted colimits can “almost” be characterized as combinations of filtered colimits and reflexive coequalizers.

## References

• P. Gabriel and F. Ulmer, Lokal präsentierbare Kategorien , Springer LNM 221, Springer-Verlag 1971
• J. Adamek, J. Rosicky, E.M. Vitale, What are sifted colimits?, TAC 23 (2010) pp. 251–260. (web)

Revised on October 7, 2012 01:24:17 by Todd Trimble (68.198.214.232)