Lax natural transformation

In the mathematical field of category theory, specifically the theory of 2-categories, a lax natural transformation is a kind of morphism between 2-functors.

Definition

Let C and D be 2-categories, and let $F,G:C\to D$ be 2-functors. A lax natural transformation $\alpha :F\to G$ between them consists of

• a morphism ${\alpha }_c:F(c)\to G(c)$ in D for every object $c\in C$ and
• a 2-morphism ${\alpha }_f:G(f)\circ {\alpha }_c\to {\alpha }_{c^{\prime }}\circ F(f)$ for every morphism $f:c\to c^{\prime }$ in C

satisfying some equations (see or )