Editing Commutative diagram (section)

==Examples==
===Example 1===
In the left diagram, which expresses the [[Isomorphism_theorems#First_isomorphism_theorem|first isomorphism theorem]], commutativity of the triangle means that <math>f = \tilde{f} \circ \pi</math>. In the right diagram, commutativity of the square means <math>h \circ f = k \circ g</math>.
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===Example 2===
In order for the diagram below to commute, three equalities must be satisfied:

# <math>r \circ h \circ g = H \circ G \circ l</math>
# <math>m \circ g = G \circ l</math>
# <math>r \circ h = H \circ m</math>

Here, since the first equality follows from the last two, it suffices to show that (2) and (3) are true in order for the diagram to commute. However, since equality (3) generally does not follow from the other two, it is generally not enough to have only equalities (1) and (2) if one were to show that the diagram commutes.

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