finitary
A functor is finitary when it preserves filtered colimits.
- Dual property: cofinitary
- nLab Link
Relevant implications
- cocontinuous implies coequalizer-preserving andcoproduct-preserving andfinitary
- finitary andfinite-coproduct-preserving implies coproduct-preserving *
- finitary andright exact implies cocontinuous *
*Those implications also require assumptions on the source or target category.
Examples
There are 4 functors with this property.
- abelianization functor for groups
- forgetful functor for vector spaces
- free group functor
- identity functor on the category of sets
Counterexamples
There are 2 functors without this property.
Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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