We call square in a 2-category a quadruple of objects $A,B,X,Y$, a quadruple of morphisms $S : A \to X, T : A \to Y, U : X\to B, V : Y \to B$, and a 2-morphism $\vf : U\circ S \Rightarrow V\circ T$. Such a square will be denoted by a diagram

We will also employ the condensed notation