# Questions tagged [diagram-chasing]

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

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### Need help drawing these diagrams in category theory (sources for good diagrams would also be appreciated)

I already feel that I can better understand mathematical structures by using diagrams from category theory. The books I am reading only give me the basics and I am interested in learning how to draw ...
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### Short exact sequence of modules induces short exact sequence of cokernels

I have a commutative unital ring $A$, a short exact sequence $L\to M\to N$ of $A$-modules, a faithful exact contravariant functor $D:\text{Mod}_A\to\text{Mod}_A$ satisfying $$DM=0\iff M=0,$$ and ...
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### Basic example in diagram chasing

Consider the following diagram: Given that $h \circ f = k$ and $l \circ h = g$, prove that $g \circ f = l \circ k$ Answer: page-35, An introduction to Category Theory, Harold Simmons I am a bit ...
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### direct sum of two exact sequence is exact [duplicate]

recently I have had some problems thinking about this, does the direct sum of two exact sequence is also exact? the picture is as follows: all $M_i$ be R modules, and all map is R linear map,and the ...