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- Discussion Type
- discussion topicsubterminal object
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active 1 hour ago

- Discussion Type
- discussion topicaffine monad
- Category Latest Changes
- Started by maxsnew
- Comments 7
- Last comment by zskoda
- Last Active 4 hours ago

- Discussion Type
- discussion topicopen problems in homotopy type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 25
- Last comment by Urs
- Last Active 7 hours ago

- Discussion Type
- discussion topicGustav Lejeune Dirichlet
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active 17 hours ago

- Discussion Type
- discussion topicE. Hastings Moore
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 17 hours ago

- Discussion Type
- discussion topicbalanced monoidal category
- Category Latest Changes
- Started by nsnyder
- Comments 2
- Last comment by Urs
- Last Active 18 hours ago

Balancing doesn’t mention duals anywhere, and makes sense even without duals. I removed an incorrect statement and replaced it with the correct one. Not sure if it needs a reference, but the correct result appears as Lemma 4.20 in https://arxiv.org/pdf/0908.3347.pdf (where it’s attributed to Deligne, but the citation is to Yetter).

- Discussion Type
- discussion topiccondensed set
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 70
- Last comment by DavidRoberts
- Last Active 18 hours ago

- Discussion Type
- discussion topicbook homotopy type theory > history
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Mike Shulman
- Last Active 1 day ago

- Discussion Type
- discussion topicBook HoTT
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Mike Shulman
- Last Active 1 day ago

- Discussion Type
- discussion topicWeil-Petersson metric
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active 1 day ago

- Discussion Type
- discussion topicD'Auria-Fre formulation of supergravity
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 1 day ago

crated D'Auria-Fre formulation of supergravity

there is a blog entry to go with this here

- Discussion Type
- discussion topicjoint and marginal probability
- Category Latest Changes
- Started by PaoloPerrone
- Comments 3
- Last comment by PaoloPerrone
- Last Active 1 day ago

- Discussion Type
- discussion topicn-connected type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active 1 day ago

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- Discussion Type
- discussion topicsuper-Cartan geometry
- Category Latest Changes
- Started by David_Corfield
- Comments 29
- Last comment by Urs
- Last Active 1 day ago

I see super-Cartan geometry is taking shape. Will Clifford algebras make an appearance in the The super-Klein geometry: super-Minkowski spacetime section?

Is there a higher super-Cartan way of thinking about what is at 3-category of fermionic conformal nets, about the String 2-group and superstrings, as here about the spin group and fermions.

- Discussion Type
- discussion topicYuval Ne'eman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicpicture changing operator
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

added pointer to Catenacci-Grassi-Noja 18

- Discussion Type
- discussion topicstring theory
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active 1 day ago

I have added to string theory a new section Critical strings and quantum anomalies.

Really I was beginning to work on a new entry twisted spin^c structure (not done yet) and then I found that a summary discussion along the above lines had been missing.

- Discussion Type
- discussion topicself-dual higher gauge theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 1 day ago

started self-dual higher gauge theory. Just minimal idea and list of references so far.

- Discussion Type
- discussion topicregular hyperdoctrine
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Mike Shulman
- Last Active 2 days ago

- Discussion Type
- discussion topictopological cyclic homology
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicrepresentability determines functoriality
- Category Latest Changes
- Started by BartoszMilewski
- Comments 1
- Last comment by BartoszMilewski
- Last Active 2 days ago

- Discussion Type
- discussion topicMario Trigiante
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicAdS-CFT in condensed matter physics
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicCorina Keller
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 2 days ago

- Discussion Type
- discussion topicquantum field theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 2 days ago

wrote an Idea-section at quantum field theory

- Discussion Type
- discussion topicsupergravity
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 2 days ago

created supergravity

so far just an "Idea" section and a link to D'Auria-Fre formulation of supergravity (which i am busy working on)

- Discussion Type
- discussion topicStiefel-Whitney class
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 2 days ago

added to Stiefel-Whitney class briefly the definition/characterization.

- Discussion Type
- discussion topicsupersymmetry
- Category Latest Changes
- Started by Urs
- Comments 53
- Last comment by Urs
- Last Active 2 days ago

I’ll be working a bit on supersymmetry.

Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)

The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold $X$ which is invariant under the super-diffeomorphism group of $X$.

where you say

Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.

I think you got something mixed up here. If $X$ is spacetime, a field on $X$

*is*the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.The second complaint is after where the original entry said

many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.

You wrote:

This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.

I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.

So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.

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

- Discussion Type
- discussion topicVenkata S. R. Redrouthu
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicD=11 N=1 supergravity
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicexceptional generalized geometry
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 2 days ago

added to

*exceptional generalized geometry*two examples of reductions of stucture groups that encode higher supersymmetry in 11d sugra.

- Discussion Type
- discussion topicorthogonal group
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active 2 days ago

added a table with some homotopy groups in the unstable range to

*orthogonal group – Homotopy groups*

- Discussion Type
- discussion topicidempotent monoid in a monoidal category
- Category Latest Changes
- Started by DELETED_USER_2018
- Comments 10
- Last comment by ncfavier
- Last Active 3 days ago

[deleted]

- Discussion Type
- discussion topicself-duality for pregeometric C-field -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

a bare list of references, to be

`!include`

-ed into the References-sections of relevant entries (such as*D=11 supergravit*,*supergravity C-field*,*premetric C-fields*)

- Discussion Type
- discussion topicmonoidal functor
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 3 days ago

created (finally) lax monoidal functor (redirecting monoidal functor to that) and strong monoidal functor.

Hope I got the relation to 2-functors right. I remember there was some subtlety to be aware of, but I forget which one. I could look it up, but I guess you can easily tell me.

- Discussion Type
- discussion topicField
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

Created page for Field, the category of fields. (See discussions on initial object.)

- Discussion Type
- discussion topicconfiguration space of points
- Category Latest Changes
- Started by Tim_Porter
- Comments 100
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

I fixed a link to a pdf file that was giving a general page, and not the file!

- Discussion Type
- discussion topicmultilimit
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topictrivial ring
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

Added that it’s a strict terminal object.

- Discussion Type
- discussion topicmulti-adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 24
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topiccancellative category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topicrigid object
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 52
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

started a Properties-section at Lawvere theory with some basic propositions.

Would be thankful if some experts looked over this.

Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

- Discussion Type
- discussion topiccocomplete category
- Category Latest Changes
- Started by maxsnew
- Comments 5
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topiclocally presentable category
- Category Latest Changes
- Started by Tobias Fritz
- Comments 19
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- In the definition, the article states "every object in C is a small object (which follows from 2 and 3)". The bracketed remark doesn't seem quite right to me, since neither 2 nor 3 talk about smallness of objects. Presumably this should better be phrased as in A.1.1 of HTT, "assuming 3, this is equivalent to the assertion that every object in S is small".

Am I right? I don't (yet) feel confident enough with my category theory to change this single-handedly.

- Discussion Type
- discussion topicreal closed field
- Category Latest Changes
- Started by Todd_Trimble
- Comments 20
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

I added a little bit of material to ordered field, namely that a field is orderable iff it is a real field (i.e., $-1$ is not a sum of squares). More importantly, at real closed field, I have addressed an old query of Colin Tan:

Colin: Is it true that real closure is an adjoint construction to the forgetful functor from real closed fields to orderable fields?

by writing out a proof (under Properties) that indeed the forgetful functor from category of real closed fields and field homomorphisms to the category of real fields and field homomorphisms has a left adjoint (the real closure). Therefore I am removing this query from that page over to here.

- Discussion Type
- discussion topiccartesian product
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topicalgebraic structure
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topicalgebraic category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 6
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

- Discussion Type
- discussion topicfield
- Category Latest Changes
- Started by Mike Shulman
- Comments 13
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

I added to field a mention of some other constructive variants of the definition, with a couple more references.

- Discussion Type
- discussion topicrig category
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by David_Corfield
- Last Active 4 days ago

concerning the discussion here: notice that an entry

*rig category*had once been created, already.

- Discussion Type
- discussion topicJohn D. Berman
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active 4 days ago

brief

`category:people`

-entry for hyperlinking references at*equivariant stable homotopy theory*and*enriched (infinity,1)-category theory*

- Discussion Type
- discussion topicfinitely complete > history
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 4
- Last comment by Urs
- Last Active 4 days ago

Created page for finitely complete analogue to finitely cocomplete.

- Discussion Type
- discussion topicfinitely cocomplete > history
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

clearing this old entry, making “finitely cocomplete” instead a redirect to

*finitely cocomplete category*

- Discussion Type
- discussion topicfinitely cocomplete category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicEmily Riehl
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by Samuel Adrian Antz
- Last Active 4 days ago

adding paper

- Emily Riehl,
*Could $\infty$-category theory be taught to undergraduates?*(arxiv:2302.07855)

- Emily Riehl,

- Discussion Type
- discussion topicinfinity-category
- Category Latest Changes
- Started by adeelkh
- Comments 11
- Last comment by Urs
- Last Active 5 days ago

I just added a link to Lurie's "What is...?" paper.

- Discussion Type
- discussion topicfunctoriality of categories of presheaves
- Category Latest Changes
- Started by anuyts
- Comments 8
- Last comment by anuyts
- Last Active 5 days ago

- Discussion Type
- discussion topicProf
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by anuyts
- Last Active 5 days ago