What are sifted colimits ?

Adamek, J. [Technical university Braunschweig,] Rosicky, Jiri [UCL] Vitale, Enrico [UCL]

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.