CatDat

epimorphism-preserving

A functor $F : \mathcal{C} \to \mathcal{D}$ preserves epimorphisms if every epimorphism in $\mathcal{C}$ is mapped to an epimorphism in $\mathcal{D}$.
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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