Proposition 3
Tag 0DRQ, permanent. Cite it as [Bourbaki, Tag 0DRQ].
Algebra, chapter X, § 2. Complexes de A-modules
If f and g are two homotopic morphisms from C into C′, then H(f)=H(g). Let s be a homotopy connecting f to g. One has
(g−f)(Z(C))=(d′∘s+s∘d)(Z(C))=(d′∘s)(Z(C))⊂B(C′), hence
H(g−f)=0 and
H(g)=H(f).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Cites
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