Processing math: 100%

The Stacks project

Remark 13.35.5. Let F : \mathcal{T} \to \mathcal{T}' be an exact functor of triangulated categories. Given a full subcategory \mathcal{A} of \mathcal{T} we denote F(\mathcal{A}) the full subcategory of \mathcal{T}' whose objects consists of all objects F(A) with A \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A}). We have

F(\mathcal{A}[a, b]) = F(\mathcal{A})[a, b]
F(smd(\mathcal{A})) \subset smd(F(\mathcal{A})),
F(add(\mathcal{A})) \subset add(F(\mathcal{A})),
F(\mathcal{A} \star \mathcal{B}) \subset F(\mathcal{A}) \star F(\mathcal{B}),
F(\mathcal{A}^{\star n}) \subset F(\mathcal{A})^{\star n}.

We omit the trivial verifications.


Comments (0)


Your email address will not be published.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.