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