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 $$F,G\colon C\to D$$ be 2-functors. A lax natural transformation $$\alpha\colon F\to G$$ between them consists of satisfying some equations (see or )
 * a morphism $$\alpha_c\colon F(c)\to G(c)$$ in D for every object $$c\in C$$ and
 * a 2-morphism $$\alpha_f\colon G(f)\circ\alpha_c \to \alpha_{c'}\circ F(f)$$ for every morphism $$f\colon c\to c'$$ in C