Lax functor

In category theory, a discipline within mathematics, the notion of lax functor between bicategories generalizes that of functors between categories.
Let "C,D" be bicategories. We denote composition in diagrammatic order. A "lax functor P from C to D", denoted formula_1, 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 formula_6 and formula_7 above, are invertible is called a pseudofunctor.