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3. contravariant functor

Wiktionary

contravariant functor

n. (context category theory English) A functor which maps a morphism ''f'':''X'' → ''Y'' to a morphism ''F''(''f''):''F''(''Y'') → ''F''(''X''), such that if $h\; =\; g\; circ\; f$, then $F(h)\; =\; F(f)\; circ\; F(g)$.