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:
 * $\xymatrix{

A \ar[r]^\alpha \ar[d]^\gamma & B \ar[d]^\beta \\ C \ar[r]^\delta & D }$