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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2011

    at geometric morphism in the new section Structure preserved by geometric morphisms I wanted to expand on Johnstone’s remark B2.2.7 on how geometric morphisms preserve the characteristic well-powerdness of toposes as indexed categories over themselves. I have started at indexed category a section on well-poweredness for that purpose, but I have to leave things in very incomplete form for the moment.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 27th 2011
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2011

    I have been expanding geometric morphism by statements and proofs of various basic facts, mostly in the section between presheaf toposes.

    (I am using this as lecture notes in an introductory course.)

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 18th 2018

    Added reference to the Elephant where it is proved that Loc(X,Y)Topos(Sh(X),Sh(Y))Loc(X,Y) \to Topos(Sh(X),Sh(Y)) is an equivalence of categories, where the former is given the canonical poset structure.

    diff, v54, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJan 22nd 2019

    Fix order of functors in change-of-base adjunction.

    diff, v55, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2020

    added cross-link with natural homotopy

    diff, v56, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2022

    This page is lacking original historical references. What’s an original reference for the idea that maps of topological spaces generalize to geometric morphisms between toposes?

    diff, v60, current