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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.
@article{TAC_2010_23_a12, author = {J. Adamek and J. Rosicky and E. M. Vitale}, title = {What are sifted colimits?}, journal = {Theory and applications of categories}, pages = {251--260}, publisher = {mathdoc}, volume = {23}, year = {2010}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TAC_2010_23_a12/} }
J. Adamek; J. Rosicky; E. M. Vitale. What are sifted colimits?. Theory and applications of categories, The Bourn Festschrift, Tome 23 (2010), pp. 251-260. http://geodesic.mathdoc.fr/item/TAC_2010_23_a12/