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 ${\displaystyle F(f\circ g)=F(f)\circ F(g)}$ and ${\displaystyle F(1)=1}$ 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