C-valued sheaves | Higher Topos Theory notes

Remark 6.147.

Recall that the category $\FunR(C\catop,T)$ is the Lurie tensor product $C \otimes T$ in $\PrL$ , which in turn may be written as $\FunR(T\catop,C)$ . We denote this category by $\Shv_C(T)$ and call it the category of $$C$$ -valued sheaves on $$T$$ . Keeping track of the functoriality in $$T$$ shows that the topos $\Fun^{\omega}(C,\An)$ classifies $$C$$ -valued sheaves.