Commutative diagram

Summary

A commutative diagram is a drawing of objects and morphisms of a category. In it, any two directed paths with the same start and the same end compose to the same morphism. Diagrams are the main notation of category theory and homological algebra: one picture records many equations between composites. The commutative square $g \circ f = k \circ h$ and the commutative triangle $g \circ f = h$ are the basic shapes. The definition of a natural transformation is the commutativity of one square for each morphism.