In mathematics, and especially in category theory, a **commutative diagram** is a diagram of objects (also known as *vertices*) and morphisms (also known as *arrows* or *edges*) such that all directed paths in the diagram with the same start and endpoints lead to the same result by composition. Commutative diagrams play the role in category theory that equations play in algebra (see Barr-Wells, Section 1.7).

Note that a diagram may not be commutative, i.e., the composition of different paths in the diagram may not give the same result. For clarification, phrases like "this commutative diagram" or "the diagram commutes" may be used.

Read more about Commutative Diagram: Examples, Verifying Commutativity, Diagram Chasing, Diagrams As Functors

### Famous quotes containing the word diagram:

““God’s fire upon the wane,

A *diagram* hung there instead,

More women born than men.””

—William Butler Yeats (1865–1939)