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- Discussion Type
- discussion topicmodular form
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 5 hours ago

added to

*modular form*a brief paragraph with a minimum of information on modular forms*As automorphic forms*. Needs to be expanded.

- Discussion Type
- discussion topicbifunctor
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by nLab edit announcer
- Last Active 6 hours ago

I noticed that an entry

*bifunctor*was still missing, though requested by some existing entries. So I briefly added something.

- Discussion Type
- discussion topicinternal set theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 11
- Last comment by Richard Williamson
- Last Active 10 hours ago

- Discussion Type
- discussion topicShahn Majid
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 13 hours ago

- Discussion Type
- discussion topicTomasz Brzezinski
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active 13 hours ago

- Discussion Type
- discussion topicJoost Vercruysse
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Tim_Porter
- Last Active 14 hours ago

- Discussion Type
- discussion topicfunding of the nLab
- Category Latest Changes
- Started by Richard Williamson
- Comments 2
- Last comment by Urs
- Last Active 16 hours ago

Describing the arrangements which have been made for funding of the nLab in collaboration with the Topos Institute. The page, linked to from the home page, is intended to be fairly general; specific requests for donations can be made elsewhere.

- Discussion Type
- discussion topicenriched bicategory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Théo de Oliveira S.
- Last Active 20 hours ago

have created enriched bicategory in order to help Alex find the appropriate page for his notes.

- Discussion Type
- discussion topicsimplex category
- Category Latest Changes
- Started by FinnLawler
- Comments 21
- Last comment by Richard Williamson
- Last Active 23 hours ago

Some tidying up and additions at simplex category, in particular a section on its 2-categorical structure, and more on universal properties.

I’ve edited the definition to focus more on the augmented simplex category $\Delta_a$ instead of the ’topologists’ $\Delta$’, but I haven’t changed their names, because it seemed to me that that was the best way to keep everyone involved in the discussion at that page happy. (I also changed the ordinal sum functor from $+$ to $\oplus$, after Tim’s suggestion.)

- Discussion Type
- discussion topicLaiachi El Kaoutit
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by zskoda
- Last Active 1 day ago

- Discussion Type
- discussion topiccoring
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by zskoda
- Last Active 1 day ago

New sections at coring:

- base extension of corings
- morphisms in the 1-category of corings over variable base rings.

- Discussion Type
- discussion topiclocal Langlands conjecture
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 7
- Last comment by David_Corfield
- Last Active 1 day ago

This article has a weird claim on top, highlighted in yellow (see the second line):

Redirected from “local Langlands correspondence”.

Note: local Langlands conjecture and local Langlands conjecture both redirect for “local Langlands correspondence”.

- Discussion Type
- discussion topicmodel structure on relative categories
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 9
- Last comment by Hurkyl
- Last Active 1 day ago

- Discussion Type
- discussion topicalgebraic cobordism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 1 day ago

added pointer to

Victor Snaith,

*Algebraic Cobordism and K-theory*, Mem. Amer. Math. Soc. no 221 (1979)Victor Snaith,

*Towards algebraic cobordism*, Bull. Amer. Math. Soc. 83 (1977), 384-385 (doi:10.1090/S0002-9904-1977-14281-X)

Also tried to fix the ordering of the rest of the reference, but I give up for the moment. This needs attention by some expert

- Discussion Type
- discussion topicVictor Snaith
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

There was a big chunk of technical discussion on this page. I am moving this to

*algebraic cobordism*, where it belongs.

- Discussion Type
- discussion topicMarkus Dierigl
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

brief

`category:people`

-entry for hyperlinking references at*swampland cobordism conjecture*

- Discussion Type
- discussion topicMiguel Montero
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

brief

`category:people`

-entry for hyperlinking references at*swampland cobordism conjecture*

- Discussion Type
- discussion topicJacob McNamara
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

brief

`category:people`

-entry for hyperlinking references at*swampland cobordism conjecture*

- Discussion Type
- discussion topicswampland cobordism conjecture -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

This is a bare list of references, to be

`!include`

-ed into relevant entries, such as at*swampland*and*24 branes transverse to K3*, for ease of cross-linking and updating.I am taking the liberty of including a pointer to our upcoming

*M/F-Theory as Mf-Theory*which has some details on a precise version of the conjecture and a proof (from Hypothesis H).

- Discussion Type
- discussion topicLaurent Fargues
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active 1 day ago

- Discussion Type
- discussion topicHomePage
- Category Latest Changes
- Started by Urs
- Comments 62
- Last comment by Richard Williamson
- Last Active 1 day ago

I have added at

*HomePage*in the section*Discussion*a new sentence with a new link:If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.

I had completly forgotton about that page

*Welcome to the nForum (nlabmeta)*. I re-doscivered it only after my recent related comment here.

- Discussion Type
- discussion topicStefaan Caenepeel
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active 1 day ago

- Discussion Type
- discussion topicFRW model
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Hovards
- Last Active 1 day ago

some basics at

*FRW model*(in cosmology)

- Discussion Type
- discussion topicdiscrete object classifier
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicMartin-Löf dependent type theory
- Category Latest Changes
- Started by Zhen Lin
- Comments 24
- Last comment by Guest
- Last Active 2 days ago

I started an article about Martin-Löf dependent type theory. I hope there aren't any major mistakes!

One minor point: I overloaded $\mathrm{cases}$ by using it for both finite sum types and dependent sum types. Can anyone think of a better name for the operation for finite sum types?

- Discussion Type
- discussion topicmicrobundle
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active 2 days ago

Tim Porter added references to microbundle and I edited the formatting of the entry a bit

- Discussion Type
- discussion topicMilnor slide trick
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active 2 days ago

Removed the following discussion to the nForum:

Zoran Škoda: But there is much older and more general theorem of Hurewitz: if one has a map $p:E\to B$ and a numerable covering of $B$ such that the restrictions $p^{-1}(U)\to U$ for every $U$ in the covering is a Hurewicz fibration then $p$ is also a Hurewicz fibration. But the proof is pretty complicated. For example George Whitehead’s

*Elements of homotopy theory*is omitting it (page 33) and Postnikov is proving it (using the equivalent “soft” homotopy lifting property).Todd Trimble: Yes, I am aware of it. You can find a proof in Spanier if you’re interested. I’ll have to check whether the Milnor trick (once I remember all of it) generalizes to Hurewicz’s theorem.

Stephan: I wonder if this trick moreover generalizes (in a homotopy theoretic sense) to categories other that $\Top$; for example to the classical model structure on $Cat$?

- Discussion Type
- discussion topicadjoint (infinity,1)-functor
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Hurkyl
- Last Active 2 days ago

polished and expanded adjoint (infinity,1)-functor

- Discussion Type
- discussion topic(∞,1)-end
- Category Latest Changes
- Started by Hurkyl
- Comments 2
- Last comment by Hurkyl
- Last Active 2 days ago

- Discussion Type
- discussion topiccentral bimodule
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 2 days ago

- Discussion Type
- discussion topicrelative (infinity,1)-limit
- Category Latest Changes
- Started by Tim Campion
- Comments 4
- Last comment by Tim Campion
- Last Active 2 days ago

Added some basic examples from HTT. There doesn’t seem to be a page for the corresopnding 1-categorical notion. This notion is used pretty heavily in $\infty$-category theory, but it’s not so familiar from 1-category theory. But I’d have to think a 1-categorical treatment exists

*somewhere*, right?

- Discussion Type
- discussion topicextension
- Category Latest Changes
- Started by zskoda
- Comments 27
- Last comment by zskoda
- Last Active 2 days ago

- Discussion Type
- discussion topicPontryagin-Thom construction -- references
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 2 days ago

this is a bare list of references, to be

`!include`

-ed into relevant entries(various parts of this list have been contained at

*Cohomotopy*,*Cohomotopy charge map*,*Thom’s theorem*,*Pontryagin-Thom construction*and elsewhere; this here now to ease harmonizing/completing these lists)

- Discussion Type
- discussion topicleft adjoint
- Category Latest Changes
- Started by Adam Chalcraft
- Comments 5
- Last comment by Richard Williamson
- Last Active 2 days ago

- (This is my first foray into nLab, so sorry if I'm making elementary errors.)

In the definition of left adjoint of a functor U:C→ D, the claim is that it's a functor F:D → C s.t. ∃ natural transformations

ι:id_C → F;U

ϵ:U;F → id_D

But F;U is a morphism in D and U;F is a morphism in C.

Is something wrong here, have I misunderstood the notation F;U, is there a more general version of a natural transformation being used here, or what?

Thank you.

- Discussion Type
- discussion topiccircle type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicfull image
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active 3 days ago

- Discussion Type
- discussion topicstem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

thought we needed

*stem*.Also added more references at

*stable homotopy groups of spheres*

- Discussion Type
- discussion topicunit of an adjunction
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by varkor
- Last Active 3 days ago

The entry

*unit of an adjunction*had a big chunk of mixed itex+svg code at the beginning to display an adjunction. On my machine though the output of that code was ill typeset. So I have removed the code and replaced it by plain iTex encoding of an adjunction.(Just in case anyone deeply cares about the svg that was there. It’s still in the history. If it is preferred by anyone, it needs to be fixed first.)

- Discussion Type
- discussion topicsecond stable homotopy group of spheres
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 3 days ago

starting something, to go along with

*first stable homotopy group of spheres*and*third stable homotopy group of sphere*– but for the moment just collecting references

- Discussion Type
- discussion topicsuspension type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 3 days ago

- Discussion Type
- discussion topicstable splitting of mapping spaces
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by nLab edit announcer
- Last Active 3 days ago

- Discussion Type
- discussion topicThomason model structure
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Hurkyl
- Last Active 3 days ago

Idea-section and one further reference at Thomason model structure.

I remember Mike once said on the blog somewhere that there might be some problem with Thomason's original claim that cofibrant objects in this structure are posets. I made a brief remark on this, but I can't find Mike's original comment.

- Discussion Type
- discussion topiccondensed cohesion
- Category Latest Changes
- Started by David_Corfield
- Comments 21
- Last comment by David_Corfield
- Last Active 3 days ago

- Discussion Type
- discussion topictwisted arrow (∞,1)-category
- Category Latest Changes
- Started by Hurkyl
- Comments 1
- Last comment by Hurkyl
- Last Active 4 days ago

Created an entry for this.

I’ve adopted the existing convention at nLab in the definition of $Tw(C)$ (which is also the definition I prefer).

Since the opposite convention is used a lot (e.g. by Lurie), I’ve decided it was worth giving it notation, the relation between the versions, and citing results in both forms. Since I didn’t have any better ideas, I’ve settled on $\overline{Tw}(C)$.

- Discussion Type
- discussion topiclax (∞,1)-colimit
- Category Latest Changes
- Started by Hurkyl
- Comments 2
- Last comment by Hurkyl
- Last Active 4 days ago

I added the description of lax (co)limits of Cat-valued functors via (co)ends and ordinary (co)limits. I should probably flesh this out more.

I’ve adopted the convention on twisted arrows at twisted arrow category, which is opposite of that in GNN.

In the case of ordinary 2-category, when the diagram category is a 1-category, is the expression of lax (co)limits via ordinary weighted (co)limits really as simple as taking the weights $C_{\bullet/}$ or $C_{/\bullet}$? I can’t find a reference that spells that out clearly; if there really is such a simple description it should be put on the lax (co)limit page.

- Discussion Type
- discussion topicorbifold cohomology
- Category Latest Changes
- Started by Urs
- Comments 102
- Last comment by David_Corfield
- Last Active 4 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 topicM2-M5 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicAdS-CFT
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicp-adic AdS/CFT correspondence
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicinjective object
- Category Latest Changes
- Started by Todd_Trimble
- Comments 21
- Last comment by Todd_Trimble
- Last Active 4 days ago

Added material to injective object, including a proof of Baer’s criterion for injective modules, and the result that for modules over Noetherian rings, direct sums of injective modules are injective.

- Discussion Type
- discussion topiclocale
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Dmitri Pavlov
- Last Active 5 days ago

added to locale a section relation to toposes stating localic reflection

- Discussion Type
- discussion topicThompson sporadic group
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active 5 days ago

- Discussion Type
- discussion topicclosed functor
- Category Latest Changes
- Started by Keith Harbaugh
- Comments 1
- Last comment by Keith Harbaugh
- Last Active 5 days ago

- Discussion Type
- discussion topic(infinity,1)-category of (infinity,1)-categories
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Hurkyl
- Last Active 5 days ago

have added pointer to

Charles Rezk,

*A model for the homotopy theory of homotopy theory*, Trans. Amer. Math. Soc. 353 (2001), 973-1007 (arXiv:math/9811037, doi:10.1090/S0002-9947-00-02653-2)Julia Bergner,

*Three models for the homotopy theory of homotopy theories*, Topology Volume 46, Issue 4, September 2007, Pages 397-436 (arXiv:math/0504334, doi:10.1016/j.top.2007.03.002)

- Discussion Type
- discussion topichadrons as KK-modes of 5d Yang-Mills theory -- references
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicHyungrok Kim
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicTommaso Macrelli
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicclassical double copy
- Category Latest Changes
- Started by Luigi
- Comments 15
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicquantum anomaly
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 5 days ago

added to quantum anomaly

an uncommented link to Liouville cocycle

a paragraph with the basic idea of fermioninc anomalies

the missing reference to Witten’s old article on spin structures and fermioninc anomalies.

The entry is still way, way, stubby. But now a little bit less than a minute ago ;-

- Discussion Type
- discussion topicinfinity-groupoid
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 25
- Last comment by Urs
- Last Active 6 days ago