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→In Pure Mathematics: Mention contravariance. Mathematical functors are cool; computer language functors less so.
:<math>F(g \circ f) = F(g) \circ F(f)</math>.
:<math>F(g \circ f) = F(g) \circ F(f)</math>.
Functors are the fundamental objects used to relate structures between different categories.
Functors are the fundamental objects used to relate structures between different categories.
The above is sometimes called a "covariant functor", to distinguish it from the less common "contravariant functor". In a contravariant functor, the composition order is reversed:
:<math>F(g \circ f) = F(f) \circ F(g)</math>.
=== Examples ===
=== Examples ===