trivial coverage

**(trivial coverage)**

For $\mathcal{C}$ a small category, the *trivial coverage* is the coverage with no covering families at all, meaning that the sheaf condition over the resulting site is empty, in that *every* presheaf is a sheaf for this coverage.

Hence the category of presheaves $[\mathcal{C}^{op},Set]$ over a site $\mathcal{C}_{triv}$ with trivial coverage is already the corresponding category of sheaves, hence the corresponding sheaf topos:

$Sh\left( \mathcal{C}_{triv}\right)
\;\simeq\;
[\mathcal{C}^{op}, Set]
\,.$

Created on June 14, 2018 at 11:23:26. See the history of this page for a list of all contributions to it.