pseudofunctor

From pseudo- +‎ functor.

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pseudofunctor (plural pseudofunctors)

1. (mathematics) A mapping between categories that is just like a functor except that ${\displaystyle f(x\circ y)=f(x)\circ f(y)}$ and ${\displaystyle f(1)=1}$ do not hold as exact equalities but only up to coherent isomorphisms.