The basic commutative diagrams are:

A -> B       A -> B
| | and \ |
v v v v
C -> D C
To say that a diagram is commutative means the following. Suppose x is in A, and let A -> C -> ... -> B and A -> D -> ... -> B be two ways of chasing arrows, or paths, around the diagram (only going forward on the arrows). Then if the first path leads to y in C, the second path leads to the same y.

For example, let f be a map from A to B, g be a map from B to C, and h be a map from A to C. If the diagram

A -> B
\ |
v v
commutes, then for any x in A, h(x)=g(f(x)).

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