Definition 13.40.1. Let $\mathcal{D}$ be an additive category. Let $\mathcal{A} \subset \mathcal{D}$ be a full subcategory. The right orthogonal $\mathcal{A}^\perp $ of $\mathcal{A}$ is the full subcategory consisting of the objects $X$ of $\mathcal{D}$ such that $\mathop{\mathrm{Hom}}\nolimits (A, X) = 0$ for all $A \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$. The left orthogonal ${}^\perp \mathcal{A}$ of $\mathcal{A}$ is the full subcategory consisting of the objects $X$ of $\mathcal{D}$ such that $\mathop{\mathrm{Hom}}\nolimits (X, A) = 0$ for all $A \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A})$.
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)
There are also: