Category theory MOC

Completeness and cocompleteness

A category 𝖢 is said to be #m/def/cat

• finitely (co)complete iff for every finite category 𝖩, 𝖢 has all 𝖩-(co)limits.
• (co)complete iff for every small category 𝖩, 𝖢 has all 𝖩-(co)limits.

If 𝖢 is both (finitely) complete and (finitely) cocomplete, it is called (finitely) bicomplete.

Properties

1. Finite (co)completeness criteria

See also

• Exact functor
• (Co)continuous functor

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