Synthetic topos theory
[000K] Definition

Let UU be a universe. We define a morphism p:AA\mathord {\textnormal {\textsf {p}}}:\mathbb {A}_{\bullet }\rightarrow \mathbb {A} in Topos(U)\mathord {\textnormal {\textsf {Topos}}}(U) to be the one sent by Sh\mathord {\textnormal {\textsf {Sh}}} to w:wLexCocompUwLexCocompU/w{\mathord {\textnormal {\textsf {w}}}}^{*}:{\langle \mathord {\textnormal {\textsf {w}}}\rangle }_{\mathord {\textnormal {\textsf {LexCocomp}}}_{U}}\rightarrow {\langle \mathord {\textnormal {\textsf {w}}}\rangle }_{\mathord {\textnormal {\textsf {LexCocomp}}}_{U}}/\mathord {\textnormal {\textsf {w}}}.