Lemma 15.91.16. In Situation 15.91.15. For $K \in D(A)$ the object $K' = R\mathop{\mathrm{lim}}\nolimits (K \otimes _ A^\mathbf {L} K_ n^\bullet )$ is derived complete with respect to $I$.

**Proof.**
This is a special case of Lemma 15.91.14 because $f_ i^ n$ acts by an endomorphism of $K_ n^\bullet $ which is homotopic to zero by Lemma 15.28.6.
$\square$

## 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Your email address will not be published.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.

## Comments (0)

There are also: