Definition 6.10. (Sheaf category, [Lurie 2009, Definition 6.2.2.6])
Let \(C\) be a category equipped with a Grothendieck topology \(\tau\). We denote by
\[\Shv_{\tau}(C) \quad \subseteq \quad \PSh(C)\]
the full subcategory of \(\tau\)-sheaves. We denote the left exact left adjoint by
\[L_{\tau}\colon \PSh(C) \to \Shv_{\tau}(C).\]
References
- Jacob Lurie. Higher topos theory. Ann. Math. Stud. 170, Princeton, NJ: Princeton University Press. 2009.