Commutative diagram

https://en.wikipedia.org/wiki/Commutative_diagram

A commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. It is said that commutative diagrams play the role in category theory that equations play in algebra.

Commutative diagrams are a convenient way to visualize equalities of morphisms.

We often use diagrams consisting of objects and morphisms of a category. Such a diagram in a category 𝒞 is said to commute, when, for each pair of objects 𝑎 and 𝑏, any two paths leading from 𝑎 to 𝑏 yield, by composition, equal morphisms from 𝑎 to 𝑏.

Moreover, commutative diagrams are closed under composition of diagrams in that a diagram commutes if all of its subdiagrams commute.

Saying a diagram commutes means that for all pairs of vertices, all paths from between them are equivalent, i.e. correspond to the same arrow of the category.