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Questions tagged [diagram-chasing]

For questions about proofs using equivalent map compositions in commutative diagrams in homological algebra, or in category theory in general.

20
votes
1answer
626 views

Is there a computer program that does diagram chases?

After having done many tedious, robotic proofs that various arrows in a given diagram have certain properties, I've begun to wonder whether or not someone has made this automatic. You should be able ...
22
votes
4answers
2k views

Short exact sequence of exact chain complexes

If $0 \rightarrow A_{\bullet} \rightarrow B_{\bullet} \rightarrow C_{\bullet} \rightarrow 0$ is a short exact sequence of chain complexes (of R-modules), then, whenever two of the three complexes $A_{\...
10
votes
1answer
334 views

Category theorists: would you use a software tool for diagramming / chasing?

Update: Source Code Repository Screenshots: Now the users can edit the default colors of arrows, nodes etc. using the ColorEditor: Users can draw diagrams and store them into a Graph Database (...
6
votes
1answer
257 views

Category theory: Enough that polygonal diagrams commute

I've read somewhere that for a categorical diagram to commute, it is enough that all its polygonal subdiagrams commute. I want a reference and a detailed proof of this. Please also give a formal ...