CatDat

coequalizer-preserving

A functor $F$ preserves coequalizers when for every parallel pair of morphisms $f,g : A \to B$ whose coequalizer $p : B \to Q$ exists, also $F(p) : F(B) \to F(Q)$ is an coequalizer of $F(f),F(g) : F(A) \to F(B)$.

• Dual property: equalizer-preserving

Relevant implications

• cocontinuous implies coequalizer-preserving andcoproduct-preserving andfinitary
• coequalizer-preserving andconservative implies faithful *
• coequalizer-preserving andcoproduct-preserving implies cocontinuous *
• coequalizer-preserving andfinite-coproduct-preserving implies right exact *

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

Examples

There are 3 functors with this property.

• abelianization functor for groups
• free group functor
• identity functor on the category of sets

Counterexamples

There are 3 functors without this property.

• contravariant power set functor
• covariant power set functor
• forgetful functor for vector spaces

Unknown

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

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