Contravariant Functor

up:: Functor

A contravariant functor is a functor which flips morphisms in the target Category. It’s usually denoted as

where is the Opposite Category of .

Thus, formally, for each , we have that

i.e. morphisms are flipped upon ‘s influence.

Examples

• When talking about Vector Spaces and their relation to their Vector Space Duals, it can be proven that The functor between vector spaces and their duals is contravariant.

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References

• What is a Functor? Definitions and Examples, Part 2