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In mathematics, a pseudofunctor F is a mapping between 2-categories, or from a category to a 2-category, that is just like a functor except that F = F ∘ F {\displaystyle F=F\circ F} and F = 1 {\displaystyle F=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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