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- Discussion Type
- discussion topicgroup T-complex
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 3 days ago

- Discussion Type
- discussion topicTully-Fisher relation
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicsimplicial T-complex and algebraic Kan complexes
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Tim_Porter
- Last Active 3 days ago

Because of the algebraic Kan complex entry I had a look at the simplicial T-complex page. I am not sure that the current page is quite right in its wording. It is a bit the age old problem of structure or properties. In the algebraic Kan complex, the filler choice function is part of the structure. In a T-complex the thin elements form part of the structure but then properties of the thin elements show that there is a unique choice function taking thin values. They then satisfy some equational conditions.

My thought would be that there should be a bit more precision on the differences between them. For instance I think it is true (but I would need to prove it in detail) that any simplicial T-complex gave an algebraic Kan complex, yielding an ’inclusion functor’ from SimpT to Alg Kan. That functor should have a left adjoint which kills off the Whitehead products etc, (that need not be trivial for an algebraic Kan complex but are for a simplicial T-complex). I do not see how to construct this explicitly but am sure there must be a simple way of imposing conditions on an alg. Kan complex and looking at ’varieties’ in that category. (I have not read Thomas’s thesis and he may have done something related to this already.) In other words, can one impose equations on alg. Kan complexes, in this way. The present definition is more or less the free algebras case (?).

Before altering the simp. T-complex page, I thought it worth asking this question of ’varieties’ as the answer (if it is known) would influence how best to do the edit.

- Discussion Type
- discussion topicThomas Nikolaus
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Tim_Porter
- Last Active 3 days ago

Thomas's guest post at cafe and his paper should maybe be reflected in entry infinity-category and other places in nlab where various "models" fro infinity categories are listed, as it should have a very important role in my opinion, but still better experts should do carefully these changes. I might give a slightly uninformed interepretation of the role of this work in comparison to the experts like Mike.

- Discussion Type
- discussion topicgalaxy rotation curve
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicGrothendieck construction
- Category Latest Changes
- Started by Urs
- Comments 31
- Last comment by Mike Shulman
- Last Active 4 days ago

added to Grothendieck construction a section Adjoints to the Grothendieck construction

There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

- Discussion Type
- discussion topiccubical-type model category
- Category Latest Changes
- Started by Ulrik
- Comments 15
- Last comment by Mike Shulman
- Last Active 4 days ago

Initial stub to record some references. Wanted by type theoretic model category

- Discussion Type
- discussion topicstring field theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by nLab edit announcer
- Last Active 5 days ago

I have started adding references to

*string field theory*, in particular those by Jim Stasheff et al. on the role of L-infinity algebra and A-infinity algebra. Maybe I find time later to add more details.

- Discussion Type
- discussion topiccubical type theory
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Alizter
- Last Active 5 days ago

started

*cubical type theory*using a comment by Jonathan Sterling

- Discussion Type
- discussion topicmodel structure on sections
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active 5 days ago

- Discussion Type
- discussion topicGrothendieck construction for model categories
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Mike Shulman
- Last Active 5 days ago

I have given

*Grothendieck construction for model categories*its own entry, in order to have a place for recording references. In particular I added pointer to the original references (Roig 94, Stanculescu 12)(There used to be two places in the entry

*Grothendieck construction*where an attempt was made to list the literature on the model category version, but they didn’t coincide and were both inclomplete. So I have replaced them with pointers to the new entry.)

- Discussion Type
- discussion topicPoisson-Lie T-duality
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 6 days ago

started a bare minimum at

*Poisson-Lie T-duality*, for the moment just so as to have a place to record the two original references

- Discussion Type
- discussion topicdouble field theory
- Category Latest Changes
- Started by Luigi
- Comments 12
- Last comment by nLab edit announcer
- Last Active 6 days ago

Hello,

I noticed DFT page has not been updated in a while and I added a couple of sections: some sketchy introductory material (analogy between Kaluza-Klein and DFT) and a little insight about a more rigorous geometrical formulation of DFT.

It is still quite sketchy but I would be happy to refine it.

PS: this is my first edit, I hope I played by the rules. And thank you all for this wiki

Luigi

- Discussion Type
- discussion topictopological vector bundle
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 6 days ago

I have spelled out the proofs that over a paracompact Hausdorff space every vector sub-bundle is a direct summand, and that over a compact Hausdorff space every topological vector bundle is a direct summand of a trivial bundle, here

- Discussion Type
- discussion topichomotopy theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 16
- Last comment by David_Corfield
- Last Active 6 days ago

I have deleted an old out of date query box from homotopy theory.

- Discussion Type
- discussion topicmodel structure on functors
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Mike Shulman
- Last Active 7 days ago

expanded model structure on functors by adding a long list of properties

- Discussion Type
- discussion topicPin(2)
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicdihedral group
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topichilb category > history
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicorbifold cohomology
- Category Latest Changes
- Started by Urs
- Comments 56
- Last comment by David_Corfield
- Last Active 7 days ago

added references by Pronk-Scull and by Schwede, and wrote an Idea-section that tries to highlight the expected relation to global equivariant homotopy theory. Right now it reads like so:

On general grounds, since orbifolds $\mathcal{G}$ are special cases of stacks, there is an evident definition of cohomology of orbifolds, given by forming (stable) homotopy groups of derived hom-spaces

$H^\bullet(\mathcal{G}, E) \;\coloneqq\; \pi_\bullet \mathbf{H}( \mathcal{G}, E )$into any desired coefficient ∞-stack (or sheaf of spectra) $E$.

More specifically, often one is interested in viewing orbifold cohomology as a variant of Bredon equivariant cohomology, based on the idea that the cohomology of a global homotopy quotient orbifold

$\mathcal{G} \;\simeq\; X \sslash G \phantom{AAAA} (1)$for a given $G$-action on some manifold $X$, should coincide with the $G$-equivariant cohomology of $X$. However, such an identification (1) is not unique: For $G \subset K$ any closed subgroup, we have

$X \sslash G \;\simeq\; \big( X \times_G K\big) \sslash K \,.$This means that if one is to regard orbifold cohomology as a variant of equivariant cohomology, then one needs to work “globally” in terms of

*global equivariant homotopy theory*, where one considers equivariance with respect to “all compact Lie groups at once”, in a suitable sense.Concretely, in global equivariant homotopy theory the plain orbit category $Orb_G$ of $G$-equivariant Bredon cohomology is replaced by the global orbit category $Orb_{glb}$ whose objects are the delooping stacks $\mathbf{B}G \coloneqq \ast\sslash G$, and then any orbifold $\mathcal{G}$ becomes an (∞,1)-presheaf $y \mathcal{G}$ over $Orb_{glb}$ by the evident “external Yoneda embedding”

$y \mathcal{G} \;\coloneqq\; \mathbf{H}( \mathbf{B}G, \mathcal{G} ) \,.$More generally, this makes sense for $\mathcal{G}$ any orbispace. In fact, as a construction of an (∞,1)-presheaf on $Orb_{glb}$ it makes sense for $\mathcal{G}$ any ∞-stack, but supposedly precisely if $\mathcal{G}$ is an orbispace among all ∞-stacks does the cohomology of $y \mathcal{G}$ in the sense of global equivariant homotopy theory coincide the cohomology of $\mathcal{G}$ in the intended sense of ∞-stacks, in particular reproducing the intended sense of orbifold cohomology.

At least for topological orbifolds this is indicated in (Schwede 17, Introduction, Schwede 18, p. ix-x, see also Pronk-Scull 07)

- Discussion Type
- discussion topicpin group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicBV-BRST formalism
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by nLab edit announcer
- Last Active 7 days ago

started a stubby nPOV-description at the beginning of BV-BRST formalism

somebody please stop me, though, because I urgently need to be doing something else... :-)

- Discussion Type
- discussion topiclogical relation
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Pieter
- Last Active 7 days ago

I gave the entry

*logical relation*an Idea-section, blindly stolen from a pdf by Ghani that I found on the web. Please improve, I still don’t know what a “logical relation” in this sense actually is.Also, I cross-linked with

*polymorphism*. I hope its right that “parametricity” may redirect there?

- Discussion Type
- discussion topicDaniel Baumann
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

brief

`category:people`

-entry for hyperlinking references at

- Discussion Type
- discussion topicstructure formation
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topictransferred model structure
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Mike Shulman
- Last Active 7 days ago

added to transferred model structure a simple remark in a subsection Enrichement on conditions that allow to transfer also an enriched model structure.

(The example I am thinking of is transferring the sSet-enriched model structure on cosimplicial rings to one on cosimplicial smooth algebras. But I won’t type that into the entry for the moment…)

- Discussion Type
- discussion topicDavid Reutter
- Category Latest Changes
- Started by jamievicary
- Comments 2
- Last comment by DavidRoberts
- Last Active 7 days ago

- Discussion Type
- discussion topiccosmic inflation
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Feb 12th 2019

stub for

*cosmic inflation*(for the moment just to record some references)

- Discussion Type
- discussion topicM-wave
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Feb 12th 2019

started a minimum at

*M-wave*(I was after the kind of statement as cited by Chu-Isono there, but have added now a minimum of the background literature, too).

- Discussion Type
- discussion topichigher curvature correction
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Feb 12th 2019