Category theory MOC

Completeness and cocompleteness

A category is said to be #m/def/cat

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

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

Properties

1. Finite (co)completeness criterion

See also

• Exact functor
• (Co)continuous functor

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