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trivial coverage

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Definition

(trivial coverage)

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

Sh(𝒞 triv)[𝒞 op,Set]. 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.