Lemma 12.13.11. Let $\mathcal{A}$ be an abelian category.

If the maps $f, g : A^\bullet \to B^\bullet $ are homotopic, then the induced maps $H^ i(f)$ and $H^ i(g)$ are equal.

If $f : A^\bullet \to B^\bullet $ is a homotopy equivalence, then $f$ is a quasi-isomorphism.

## Comments (0)

There are also: