Editing Commutative diagram (section)

==Diagram chasing==
'''Diagram chasing''' (also called '''diagrammatic search''') is a method of [[mathematical proof]] used especially in [[homological algebra]], where one establishes a property of some morphism by tracing the elements of a commutative diagram. A proof by diagram chasing typically involves the formal use of the properties of the diagram, such as [[injective]] or [[surjective]] maps, or [[exact sequence]]s.<ref>{{Cite web|url=http://mathworld.wolfram.com/DiagramChasing.html|title=Diagram Chasing|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-11-25}}</ref> A [[syllogism]] is constructed, for which the graphical display of the diagram is just a visual aid. It follows that one ends up "chasing" elements around the diagram, until the desired element or result is constructed or verified.

Examples of proofs by diagram chasing include those typically given for the [[five lemma]], the [[snake lemma]], the [[zig-zag lemma]], and the [[nine lemma]].