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:

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