Pseudofunctor

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

The Grothendieck construction associates to a pseudofunctor a fibered category.

单词	Pseudofunctor
释义	Pseudofunctor 英语百科 Pseudofunctor In mathematics, a pseudofunctor f is a mapping between categories that is just like a functor except that $f(x \circ y) = f(x) \circ f(y)$ and $f(1) = 1$ do not hold as exact equalities but only up to coherent isomorphisms. The Grothendieck construction associates to a pseudofunctor a fibered category.
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