opposite category functor

 category theory
Notation (−)op:Cat→Cat(-)^{\op}: \Cat \to \Cat Domain category of small categoriesCodomain category of small categoriesLeft adjoint opposite category functorRight adjoint opposite category functor Related (−)op(-)^{\op} External nLab Link

This functor maps a small category C\C to its opposite category Cop\C^{\op} and a functor F:C→DF : \C \to \D to the opposite functor Fop:Cop→DopF^{\op} : \C^{\op} \to \D^{\op}.

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

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Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Indistinguishable functors

These functors in the database currently have exactly the same properties as the opposite category functor. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.