Commutative diagram

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Given a number of functions, a commutative diagram shows that in many cases, applying different functions, perhaps in a different order gives the same result;

Applying a function to A yields B. A simple diagram

Functions can be chained, Mathematician talk about composing them:

First applying f, then applying g yields C, from A.

That way, it is possible to create a new function, which first applies f, then g, and call it h

But h can of course be any other path as well. A diagram is called commutative diagram, if it doesn't matter what path is chosen to get from A to C.