View source for Pseudo-functor

{{Short description|Category mapping}}
In mathematics, a '''pseudofunctor''' ''F'' is a mapping between 2-categories, or from a [[Category (mathematics)|category]] to a 2-category, that is just like a [[Functor|functor]] except that <math>F(f \circ g) = F(f) \circ F(g)</math> and <math>F(1) = 1</math> 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, [http://users.ictp.it/~pub_off/lectures/lns001/Sorger/Sorger.pdf Lectures on moduli of principal G-bundles over algebraic curves]

== External links ==
*http://ncatlab.org/nlab/show/pseudofunctor

[[Category:Functors]]



{{Sourceattribution|Pseudo-functor}}