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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting 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 <a href="https://ncatlab.org/nlab/revision/singular+cohesion/1">v1</a>, <a href="https://ncatlab.org/nlab/show/singular+cohesion">current</a>

   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

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexDavid, 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.

   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.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 26th 2021
   • (edited Oct 26th 2021)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI 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.)

   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.)

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexLet'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. )

   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. )

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, 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. <a href="https://ncatlab.org/nlab/revision/diff/singular+cohesion/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/singular+cohesion/4">v4</a>, <a href="https://ncatlab.org/nlab/show/singular+cohesion">current</a>

   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.

   diff, v4, current

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIn 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?

   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?

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks, yes, that's what I had intended. Fixed now. <a href="https://ncatlab.org/nlab/revision/diff/singular+cohesion/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/singular+cohesion/4">v4</a>, <a href="https://ncatlab.org/nlab/show/singular+cohesion">current</a>

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

   diff, v4, current