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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 26th 2021

starting an entry (finally) on “singular cohesion”: the square of cohesions of $\infty$-presheaves over the global orbit category with values in an $\infty$-topos which itself is cohesive over $Grpd_\infty$.

Not done yet, but need to save

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 26th 2021

David, I am taking the liberty of breaking your lock of the entry, which seems to be from the moment the server took its daily nap 23 minutes ago.

Let me just add the last things I meant to add, then I am out of the edit box and you can have it.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeOct 26th 2021
• (edited Oct 26th 2021)

I was just sorting out some typos when it went to sleep. Hopefully I corrected the adjunction after

This follows formally from the full sub (2,1)-category inclusion

correctly.

(For some reason it doesn’t display when I bring it here.)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 26th 2021

Let’s see if the following displays here:

$\Singularities_{/\prec\mathbf{B}G} \underoverset {\hookleftarrow} {\overset{\tau_0}{\longrightarrow}} {\;\;\; \bot \;\;\;} G Orbits \,,$

(There was a blank line in the code, which might have confused the $n$Forum parser here. Also \boxed seems not to work here on the $n$Forum. )

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 26th 2021

Okay, I have now finished adding the minimum that I wanted to add here for the moment. There would be much more to say, clearly, but I do need to look into doing something else.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeOct 26th 2021

In the section ’Globally equivariant cohesive homotopy theory’

carries the following system of adjoint triples of adjoint modalities:

better to say adjoint quadruples at that stage, and then we see the adjoint triples of adjoint modalities in the following section?

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeOct 26th 2021

Thanks, yes, that’s what I had intended. Fixed now.