equivalence
A functor is an equivalence if it has a pseudo-inverse functor.
- Dual property: equivalence (self-dual)
- nLab Link
Relevant implications
- comonadic andfull implies equivalence
- equivalence implies cocontinuous andcomonadic andleft adjoint
- equivalence implies continuous andmonadic andright adjoint
- essentially surjective andfaithful andfull is equivalent to equivalence
- full andmonadic implies equivalence
*Those implications also require assumptions on the source or target category.
Examples
There is 1 functor with this property.
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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