nLab
sifted colimit

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Context

Limits and colimits

limits and colimits

1-Categorical

2-Categorical

(∞,1)-Categorical

Model-categorical

Contents

Definition

A sifted colimit is a colimit of a diagram D→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)
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