Editing Commutative diagram (section)

{{Short description|Collection of maps which give the same result}}
[[image:5 lemma.svg|350px|thumb|The commutative diagram used in the proof of the [[five lemma]]]]

In [[mathematics]], and especially in [[category theory]], a '''commutative diagram''' is a [[Diagram (category theory)|diagram]] such that all directed paths in the diagram with the same start and endpoints lead to the same result.<ref>{{Cite web|url=http://mathworld.wolfram.com/CommutativeDiagram.html|title=Commutative Diagram|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-11-25}}</ref> It is said that commutative diagrams play the role in category theory that [[equations]] play in [[algebra]].<ref>{{cite book
 | last1 = Mazzola | first1 = Guerino
 | last2 = Milmeister | first2 = Gérard
 | last3 = Weissmann | first3 = Jody
 | doi = 10.1007/b138337
 | isbn = 978-3-540-26937-3
 | page = 140
 | publisher = Springer
 | title = Comprehensive Mathematics for Computer Scientists 2
 | year = 2005}}</ref>