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1. • CommentRowNumber1.
   • CommentAuthorMadeleine Birchfield
   • CommentTimeMar 21st 2025
   • PermaLink
   Author: Madeleine Birchfield
   Format: MarkdownItexSome examples of graded differential cohesive (infinity,1)-toposes that I can think of: 1. Every differential cohesive (infinity,1)-topos is trivially a graded differential cohesive (infinity,1)-toposes with trivial rheonomic, bosonic, and fermionic modalities (i.e. the modalities are the identity) 2. The (infinity,1)-topos of super formal smooth infinity-groupoids is a graded differential cohesive (infinity,1)-toposes, according to the work done by Urs Schreiber. Are there any other examples of graded differential cohesive (infinity,1)-toposes?

   Some examples of graded differential cohesive (infinity,1)-toposes that I can think of:

   1. Every differential cohesive (infinity,1)-topos is trivially a graded differential cohesive (infinity,1)-toposes with trivial rheonomic, bosonic, and fermionic modalities (i.e. the modalities are the identity)

   2. The (infinity,1)-topos of super formal smooth infinity-groupoids is a graded differential cohesive (infinity,1)-toposes, according to the work done by Urs Schreiber.

   Are there any other examples of graded differential cohesive (infinity,1)-toposes?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2025
   • (edited Mar 21st 2025)
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   Author: Urs
   Format: MarkdownItexYes, that's a really good question. I have been wondering about this for a long time, but also haven't spent real energy on it for it a long time. One will want to ask that all three stages of the adjoint modalities are suitably non-degenerate. Also one may want to ask that all three of: shape modality, infinitesimal shape modality and rheonomy modality to be equivalent to localizations at some object (the last one of which then being the "superpoint" of the model, which you may have recently seen me [[schreiber:Perì Pantheōrías|chat]] about, online).

   Yes, that’s a really good question.

   I have been wondering about this for a long time, but also haven’t spent real energy on it for it a long time.

   One will want to ask that all three stages of the adjoint modalities are suitably non-degenerate.

   Also one may want to ask that all three of: shape modality, infinitesimal shape modality and rheonomy modality to be equivalent to localizations at some object (the last one of which then being the “superpoint” of the model, which you may have recently seen me chat about, online).