page_title: Mathematical diagram
section_title: Commutative diagram
hierarchical_section_title: Mathematical diagram / Specific types of mathematical diagrams / Commutative diagram
context_page_description: Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time.
context_section_description: 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 when selecting two objects any directed path through the diagram leads to the same result by composition.
  Commutative diagrams play the role in category theory that equations play in algebra.
caption: Hasse diagram.