Pseudo-functor

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

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