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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 18th 2021

    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 SetSet/Grpd Grpd_\infty is indeed essentially unique, and that the right adjoint is equivalently given by homs out of the terminal object.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorjesuslop
    • CommentTimeApr 10th 2023

    Some ideas for improvement/review:

    In idea, first line, remove the \infty prefix of the base Grpd 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 (,1)(\infty, 1)-geometric morphism. Is it the same notion as in here? If so there’s a clash of notation (\infty-topos vs (,1)(\infty, 1)-topos, \infty-functor vs (,1)(\infty, 1)-functor, etc.).