nLab
cocontinuous functor
Contents
Context
Category theory
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

fibered limit

2-Categorical
(∞,1)-Categorical
Model-categorical
Contents
Idea
A functor is cocontinuous if it preserves small colimits .

Typically one only considers cocontinuous functors whose domain and codomain are cocomplete categories (have all small colimits).

Note that $F\colon C \to D$ is cocontinuous if and only if the functor $F^{op}: C^{op} \to D^{op}$ between opposite categories is a continuous functor .

Examples

Not every functor is cocontinuous:

References
See the references at continuous functor .

Last revised on April 17, 2024 at 15:46:57.
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