Limits and colimits
limits and colimits
limit and colimit
limits and colimits by example
commutativity of limits and colimits
connected limit, wide pullback
preserved limit, reflected limit, created limit
product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum
end and coend
A sifted colimit is a colimit of a diagram where 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.
A motivating example is a reflexive coequalizer. In fact, sifted colimits can “almost” be characterized as combinations of filtered colimits and reflexive coequalizers.
See at distributivity of products and colimits.
- 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 February 16, 2015 20:08:56
by Urs Schreiber