#horseshoe_lemma
Horseshoe lemma
Homological algebra statement
In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects and to resolutions of extensions of by . It says that if an object is an extension of by , then a resolution of can be built up inductively with the nth item in the resolution equal to the coproduct of the nth items in the resolutions of and . The name of the lemma comes from the shape of the diagram illustrating the lemma's hypothesis.
Sat 24th
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