Definition:Commutative Square

Definition
Let $\CC$ be any metacategory.

A commutative square in $\CC$ consists of four objects
 * $A,B,C,D$

and four morphisms
 * $\alpha : A \to B$
 * $\beta : B \to D$
 * $\gamma : A \to C$
 * $\delta : C \to D$

such that
 * $\ds \beta \circ \alpha = \delta \circ \gamma$

Visualization
A commutative square in $\CC$ can be visualized as a commutative diagram \begin{align*} \xymatrix{ A \ar[r]^{\alpha} \ar[d]^{\gamma} & B \ar[d]^{\beta} \\ C \ar[r]^{\delta} & D } \end{align*}