A functor 
is called contravariant if it reverses the directions of arrows,
i.e., every arrow 
is mapped to an arrow 
.
Contravariant Functor
See also
Covariant Functor, Functor, HomThis entry contributed by Margherita Barile
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Cite this as:
Barile, Margherita. "Contravariant Functor." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ContravariantFunctor.html