In algebra, especially in category theory, we use so-called **commutative diagrams**. Vertices denote objects such as groups or modules. Arrows represent morphisms, which are maps between those objects. The characteristic quality of such diagrams is that they commute. This means that you get the same result by composition, no matter which directed way in the diagram you go, as long as the start point and end point are the same.

Such diagrams are used a lot for visualizing algebraic properties. Whole proofs are done by chasing through such a diagram. That's why our next recipe will deal with it. We will start with a diagram for the first isomorphism theorem in group theory.

We will use the TikZ package. While ...

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