Synthetic topos theory
[0019] Definition

Let UU be a universe and let VV be a universe strictly greater than UU. We define Sh(Topos(1)(U),V)\mathord {\textnormal {\textsf {Sh}}}(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U),V) to be the full subcategory of Fun((Topos(1)(U))op,V)\mathord {\textnormal {\textsf {Fun}}}({(\mathord {\textnormal {\textsf {Topos}}}^{(1)}(U))}^{\mathord {\textnormal {\textsf {op}}}},V) spanned by the sheaves in the sense of [0016].