nLab
bicomplete category
Redirected from "complete and cocomplete category".
Complete categories
Context
Category theory
Limits and colimits
limits and colimits
1-Categorical
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limit and colimit
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limits and colimits by example
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commutativity of limits and colimits
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small limit
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filtered colimit
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sifted colimit
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connected limit, wide pullback
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preserved limit, reflected limit, created limit
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product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum
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finite limit
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Kan extension
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weighted limit
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end and coend
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fibered limit
2-Categorical
(∞,1)-Categorical
Model-categorical
Complete categories
Definition
A category 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
where is a small category has a limit and a colimit in .
Last revised on June 22, 2024 at 12:42:16.
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