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.