CatDat

cocontinuous

A functor is cocontinuous when it preserves all small colimits.

• Dual property: continuous
• nLab Link

Relevant implications

• cocontinuous implies coequalizer-preserving andcoproduct-preserving andfinitary
• cocontinuous implies left adjoint *
• coequalizer-preserving andcoproduct-preserving implies cocontinuous *
• equivalence implies cocontinuous andcomonadic andleft adjoint
• finitary andright exact implies cocontinuous *
• left adjoint implies cocontinuous

*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.

—