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:
“If a fish is the movement of water embodied, given shape, then cat is a diagram and pattern of subtle air.”
—Doris Lessing (b. 1919)