nLab
finitely cocomplete category
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
(β,1)-Categorical
Model-categorical
Contents
Idea
A finitely cocomplete category is a category $\mathcal{C}$ which admits all finite colimits , that is a colimit for any finite diagram $F \colon \mathcal{J} \to \mathcal{C}$ .

(A category with all small colimit is called a cocomplete category ).

This is the notion formally dual to that of finitely complete categories , see there for more.

Finitely cocomplete categories are also called rex categories , although this is rarer than βlexβ for finitely complete categories .

Last revised on February 17, 2024 at 09:20:35.
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