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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 18th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI keep wanting to point to properties of the terminal geometric morphism. While we had this scattered around in various entries (such as at *[[global sections]]*, at *[[(infinity,1)-topos]]* and elsewhere -- but not for instance at *[[(infinity,1)-geometric morphism]]*) I am finally giving it its own entry, for ease of hyperlinking. So far this contains the (elementary) proofs that the geometric morphism to the base $Set$/$Grpd_\infty$ is indeed essentially unique, and that the right adjoint is equivalently given by homs out of the terminal object. <a href="https://ncatlab.org/nlab/revision/terminal+geometric+morphism/1">v1</a>, <a href="https://ncatlab.org/nlab/show/terminal+geometric+morphism">current</a>

   I keep wanting to point to properties of the terminal geometric morphism. While we had this scattered around in various entries (such as at global sections, at (infinity,1)-topos and elsewhere – but not for instance at (infinity,1)-geometric morphism) I am finally giving it its own entry, for ease of hyperlinking.

   So far this contains the (elementary) proofs that the geometric morphism to the base $Set$/$Grpd_\infty$ is indeed essentially unique, and that the right adjoint is equivalently given by homs out of the terminal object.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorjesuslop
   • CommentTimeApr 10th 2023
   • PermaLink
   Author: jesuslop
   Format: MarkdownItexSome ideas for improvement/review: In idea, first line, remove the $\infty$ prefix of the base $Grpd_\infty$. In equaiton (1), change Grp to Grpd. It'd be nice to have a mention of the simpler (1-) topos case. Even if just a link (for instance [here](https://ncatlab.org/nlab/show/geometric+morphism#global_sections_and_constant_sheaves)). I came here from [Local System](https://ncatlab.org/nlab/show/local+system#general), talking about the terminal $(\infty, 1)$-geometric morphism. Is it the same notion as in here? If so there's a clash of notation ($\infty$-topos vs $(\infty, 1)$-topos, $\infty$-functor vs $(\infty, 1)$-functor, etc.).

   Some ideas for improvement/review:

   In idea, first line, remove the $\infty$ prefix of the base $Grpd_\infty$.

   In equaiton (1), change Grp to Grpd.

   It’d be nice to have a mention of the simpler (1-) topos case. Even if just a link (for instance here).

   I came here from Local System, talking about the terminal $(\infty, 1)$-geometric morphism. Is it the same notion as in here? If so there’s a clash of notation ($\infty$-topos vs $(\infty, 1)$-topos, $\infty$-functor vs $(\infty, 1)$-functor, etc.).