Synthetic topos theory
[0016] Definition

Let \(U\) be a universe and let \(V\) be a universe strictly greater than \(U\). We say a presheaf \(A:{(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U))}^{\mathord {\textnormal {\textsf {op}}}}\rightarrow V\) is a sheaf if it takes étale colimits in \(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U)\) to limits in \(V\).