Definition 7.12.3. Let $\mathcal{C}$ be a site whose topology is subcanonical. The Yoneda embedding $h$ (see Categories, Section 4.3) presents $\mathcal{C}$ as a full subcategory of the category of sheaves of $\mathcal{C}$. In this case we call sheaves of the form $h_ U$ with $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$ representable sheaves on $\mathcal{C}$. Notation: Sometimes, the representable sheaf $h_ U$ associated to $U$ is denoted $\underline{U}$.
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Your email address will not be published.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)