nLab
sifted colimit
Context
Limits and colimits
limits and colimits

1-Categorical
limit and colimit

limits and colimits by example

commutativity of limits and colimits

small limit

filtered colimit

sifted colimit

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

finite limit

Kan extension

weighted limit

end and coend

2-Categorical
(∞,1)-Categorical
Model-categorical
Contents
Definition
A sifted colimit is a colimit of a diagram $D \to C$ where $D$ 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.

Examples
A motivating example is a reflexive coequalizer . In fact, sifted colimits can “almost” be characterized as combinations of filtered colimits and reflexive coequalizers.

Properties
See at distributivity of products and colimits .

See also
References
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 )

Last revised on February 16, 2015 at 20:08:56.
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