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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 26th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexat [[geometric morphism]] in the new section <a href="http://nlab.mathforge.org/nlab/show/geometric+morphism#StructurePreserved">Structure preserved by geometric morphisms</a> 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 <a href="http://nlab.mathforge.org/nlab/show/indexed+category#WellPoweredness">well-poweredness</a> for that purpose, but I have to leave things in very incomplete form for the moment.

   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.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 27th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added at [[geometric morphism]] a section <a href="RelationToHomomorphismOfLocales">Relation to homomorphisms of locales</a>

   have added at geometric morphism a section Relation to homomorphisms of locales

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 11th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have been expanding [[geometric morphism]] by statements and proofs of various basic facts, mostly in the section <a href="http://nlab.mathforge.org/nlab/show/geometric+morphism#BetweenPresheafToposes">between presheaf toposes</a>. (I am using this as lecture notes in an introductory course.)

   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.)

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeOct 18th 2018
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   Author: DavidRoberts
   Format: MarkdownItexAdded reference to the [[Elephant]] where it is proved that $Loc(X,Y) \to Topos(Sh(X),Sh(Y))$ is an equivalence of categories, where the former is given the canonical poset structure. <a href="https://ncatlab.org/nlab/revision/diff/geometric+morphism/54">diff</a>, <a href="https://ncatlab.org/nlab/revision/geometric+morphism/54">v54</a>, <a href="https://ncatlab.org/nlab/show/geometric+morphism">current</a>

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

   diff, v54, current

5. • CommentRowNumber5.
   • CommentAuthorvarkor
   • CommentTimeJan 22nd 2019
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   Author: varkor
   Format: MarkdownItexFix order of functors in change-of-base adjunction. <a href="https://ncatlab.org/nlab/revision/diff/geometric+morphism/55">diff</a>, <a href="https://ncatlab.org/nlab/revision/geometric+morphism/55">v55</a>, <a href="https://ncatlab.org/nlab/show/geometric+morphism">current</a>

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

   diff, v55, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded cross-link with _[[natural homotopy]]_ <a href="https://ncatlab.org/nlab/revision/diff/geometric+morphism/56">diff</a>, <a href="https://ncatlab.org/nlab/revision/geometric+morphism/56">v56</a>, <a href="https://ncatlab.org/nlab/show/geometric+morphism">current</a>

   added cross-link with natural homotopy

   diff, v56, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeDec 14th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis 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? <a href="https://ncatlab.org/nlab/revision/diff/geometric+morphism/60">diff</a>, <a href="https://ncatlab.org/nlab/revision/geometric+morphism/60">v60</a>, <a href="https://ncatlab.org/nlab/show/geometric+morphism">current</a>

   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