What are sifted colimits?

J. Adamek, J. Rosicky, E. M. Vitale

Sifted colimits, important for algebraic theories, are "almost" just the combination of filtered colimits and reflexive coequalizers. For example, given a finitely cocomplete category $\cal A$, then a functor with domain $\cal A$ preserves sifted colimits iff it preserves filtered colimits and reflexive coequalizers. But for general categories $\cal A$ that statement is not true: we provide a counter-example.

Keywords: sifted colimit, reflexive coequalizer, filtered colimit

2000 MSC: 18A30, 18A35

Theory and Applications of Categories, Vol. 23, 2010, No. 13, pp 251-260.

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