# 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.

http://www.tac.mta.ca/tac/volumes/23/13/23-13.dvi
http://www.tac.mta.ca/tac/volumes/23/13/23-13.ps
http://www.tac.mta.ca/tac/volumes/23/13/23-13.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/13/23-13.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/13/23-13.ps

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