nLab
bicomplete category
Complete categories
Context
Category theory
category theory
Concepts
Universal constructions
Theorems
Extensions
Applications
Limits and colimits
limits and colimits
1Categorical

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
2Categorical
(∞,1)Categorical
Modelcategorical
Complete categories
Definition
A category $C$ is bicomplete if it is both a complete category as well as a cocomplete category, hence if it has all small limits and colimits: that is, if every small diagram
$F: D \to C$
where $D$ is a small category has a limit and a colimit in $C$.
Created on May 2, 2020 at 00:24:10.
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