In category theory, a discipline within mathematics, the notion of lax functor between bicategories generalizes that of functors between categories.
We denote composition in diagrammatic order.
A lax functor P from C to D, denoted
, consists of the following data: These must satisfy three commutative diagrams, which record the interaction between left unity, right unity, and associativity between C and D. See http://ncatlab.org/nlab/show/pseudofunctor.
A lax functor in which all of the structure 2-morphisms, i.e. the