CatDat

exact

A functor is exact when it is left exact and right exact.

• Dual property: exact (self-dual)
• nLab Link

Relevant implications

• exact is equivalent to left exact andright exact

*Those implications also require assumptions on the source or target category.

Examples

There is 1 functor with this property.

• identity functor on the category of sets

Counterexamples

There are 5 functors without this property.

• abelianization functor for groups
• contravariant power set functor
• covariant power set functor
• forgetful functor for vector spaces
• free group functor

Unknown

There are 0 functors for which the database has no information on whether they satisfy this property.

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