Commutative Diagram/Examples/Arbitrary Example 1

Example of Commutative Diagram
Let $A, B, X, Y$ be arbitrary sets.

Let:

be mappings such that:
 * $\beta \circ f = g \circ \alpha = k$

where $\circ$ denotes composition of mappings.

This can be depicted using the following commutative diagram:


 * $\begin{xy} \xymatrix@L+2mu@+1em{

A \ar[r]^*{\alpha} \ar[d]_*{f} \ar[rd]^*{k} & B \ar[d]^*{g} \\ X \ar[r]^*{\beta} & Y }\end{xy}$