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• CommentRowNumber101.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 21st 2021

Ok, with your encouragement I’ll give it a go.

• CommentRowNumber102.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 25th 2021

Peter Scholze has replied to my MO question. That’s right my response that a stable object in a $\infty$-topos that is relative cohesive over condensed $\infty$-groupoids (or pyknotic ones anyway) should generate a fracture square?

• CommentRowNumber103.
• CommentAuthorUrs
• CommentTimeMar 9th 2021

added brief commentary around the references by Schwede (suggesting regarding orbifold cohomology in global homotopy theory) and Juran (spellign it out)

• CommentRowNumber104.
• CommentAuthorUrs
• CommentTimeOct 26th 2021
• (edited Oct 26th 2021)

I have removed the bulk of the entry, since that was a set of notes which has meanwhile evolved into polished form in arXiv:2008.01101, while what remained here had meanwhile become notationally inconsistent with both that and related $n$Lab entries, to the extent that it now would have been serious work to adjust notation.

So I just removed it for the time being, but added more prominent cross-links with the new entries singular cohesion and singular-smooth infinity-groupoid.