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.
See also
Lax functor
Prestack (an example of pseudofunctor)
Fibered category
References
C. Sorger, Lectures on moduli of principal G-bundles over algebraic curves
External links
http://ncatlab.org/nlab/show/pseudofunctor
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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