The Stacks project

Lemma 12.14.5. Notation and assumptions as in Lemma 12.14.4 above. The morphism of complexes $\delta (s) : C_\bullet \to A[-1]_\bullet $ induces the maps

\[ H_ i(\delta (s)) : H_ i(C_\bullet ) \longrightarrow H_ i(A[-1]_\bullet ) = H_{i - 1}(A_\bullet ) \]

which occur in the long exact homology sequence associated to the short exact sequence of chain complexes by Lemma 12.13.6.

Proof. Omitted. $\square$

Comments (0)

There are also:

  • 2 comment(s) on Section 12.14: Homotopy and the shift functor

Post a comment

Your email address will not be published.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.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 011E. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 12.14.5 as pdf