Komutativni dijagram — разлика између измена

 
== Praćenje dijagrama ==
'''Praćenje dijagrama''' (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.<ref>{{Cite web|url=https://mathvault.ca/math-glossary/#chasing|title=The Definitive Glossary of Higher Mathematical Jargon — Chasing|last=|first=|date=2019-08-01|website=Math Vault|language=en-US|url-status=live|archive-url=|archive-date=|access-date=2019-11-25}}</ref> 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.
 
'''Praćenje dijagrama''' (alsokoja calledse takođe naziva '''diagrammaticdijagramskom searchpretragom''') isje a method ofmetoda [[mathematical proof|matematičkog dokaza]] usedkoja especiallyse innaročito koristi u [[homological algebra|homološkoj algebri]], wheregde onese establishesuspostavlja asvojstvo propertynekog ofmorfizma some morphism by tracing the elements ofpronalazeći aelemente commutativekomutativnog diagramdijagrama.<ref>{{Cite web|url=https://mathvault.ca/math-glossary/#chasing|title=The Definitive Glossary of Higher Mathematical Jargon — Chasing|last=|first=|date=2019-08-01|website=Math Vault|language=en-US|url-status=live|archive-url=|archive-date=|access-date=2019-11-25}}</ref> ADokaz proofpomoću bydijagrama diagramobično chasinguključuje typicallyformalnu involvesupotrebu thesvojstava formaldijagrama, usekao ofšto the properties of the diagram, such assu [[injectiveИнјективно пресликавање|injektivne]] orili [[surjectiveСурјективно пресликавање|surjektivne]] mapsmape, orili [[exact sequence|tačne sekvence]]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> AKonstruiše se [[syllogismsilogizam]] isza constructed,koji forje whichgrafički theprikaz graphicaldijagrama displaysamo ofvizuelno thepomagalo. diagramIz istoga justsledi ada visualse aid.vrši It„pretraga” followselemenata thatna onedijagramu, endssve updok "chasing"se elementsne aroundkonstruiše theili diagram,potvrdi until the desiredželjeni element or result is constructed orili verifiedrezultat.
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]].
 
Primeri dokaza pomoću dijagramskog praćenja uključuju one koji se obično daju za [[five lemma|pet lema]], [[snake lemma|zmijsku lemu]], [[zig-zag lemma|zig-zag lemu]], i [[nine lemma|devet lema]].
 
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