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What is commutativity?

We say that a diagram commutes if the maps commute, i.e., in the diagram below $\alpha\circ f = g\circ \beta$.

\begin{displaymath}\xymatrix{
X\ar[r]_{f} \ar[d]_{\beta}& Y \ar[d]_{\alpha}\\
X'\ar[r]_{g} & Y'
}\end{displaymath}



Christine Devena 2003-07-25