Definition:Commutative Diagram
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Definition
A commutative diagram is a graphical technique designed to illustrate the construction of composite mappings.
It consists of:
- A collection of points representing the various domains and codomains of the mappings in question;
- Arrows representing the mappings themselves.
The diagram is properly referred to as commutative iff all the various paths from the base of one arrow to the head of another represent equal mappings.
A mapping which is claimed to exist is indicated by a dotted arrow.
Relations
A similar technique can be applied to composition of relations in general, but this is rarely seen.
Sources
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 3.4$
- George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$
- T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 5$
