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)

References

• C. Sorger, Lectures on moduli of principal G-bundles over algebraic curves

External links

• http://ncatlab.org/nlab/show/pseudofunctor