epimorphism-preserving
A functor preserves epimorphisms if every epimorphism in is mapped to an epimorphism in .
This property is useful to rule out some adjunctions.
- Dual property: monomorphism-preserving
- nLab Link
Relevant implications
- right exact implies epimorphism-preserving
*Those implications also require assumptions on the source or target category.
Examples
There are 6 functors with this property.
- abelianization functor for groups
- contravariant power set functor
- covariant power set functor
- forgetful functor for vector spaces
- free group functor
- identity functor on the category of sets
Counterexamples
There are 0 functors without this property.
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Unknown
There are 0 functors for which the database has no information on whether they satisfy this property.
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