The Clowder Project

Let

be a diagram in ${\mathsf{Cats}}_{\mathsf{2}}$.

1. 1. The left whiskering of $\alpha$ with $G$ is the natural transformation¹
   $${\text{id}}_G\star \alpha :G\circ \varphi ⟹G\circ \psi .$$
2. 2. The right whiskering of $\alpha$ with $F$ is the natural transformation²
   $$\alpha \star {\text{id}}_F:\varphi \circ F⟹\psi \circ F.$$