Loading [MathJax]/extensions/tex2jax.js

The Stacks project

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

  1. 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.

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

Proof. Omitted. $\square$


Comments (0)

There are also:

  • 5 comment(s) on Section 12.13: Complexes

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.