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- Discussion Type
- discussion topicdouble category
- Category Latest Changes
- Started by John Baez
- Comments 27
- Last comment by varkor
- Last Active Aug 8th 2024

- I added more info on pseudo double categories and double bicategories to double category. I also simplified the picture of a square, which had been bristling with scary unnecessary detail. There's a slight blemish in the left vertical arrow, which I can't see how to fix.

- Discussion Type
- discussion topicsynthetic differential geometry
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Dmitri Pavlov
- Last Active Aug 8th 2024

I worked on synthetic differential geometry:

I rearranged slightly and then expanded the "Idea" section, trying to give a more comprehensive discussion and more links to related entries. Also added more (and briefly commented) references. Much more about references can probably be said, I have only a vague idea of the "prehistory" of the subject, before it became enshrined in the textbooks by Kock, Lavendhomme and Moerdijk-Reyes.

Also, does anyone have an electronic copy of that famous 1967 lecture by Lawvere on "categorical dynamics"? It would be nice to have an entry on that, as it seems to be a most visionary and influential text. If I understand right it gave birth to topos theory, to synthetic differential geometry and all that just as a spin-off of a more ambitious program to formalize physics. If I am not mistaken, we are currently at a point where finally also that last bit is finding a full implmenetation as a research program.

- Discussion Type
- discussion topicrelative adjoint functor
- Category Latest Changes
- Started by Peter Heinig
- Comments 5
- Last comment by RodMcGuire
- Last Active Aug 6th 2024

Made some some small improvements (ordering of sections, note on how the definition defaults to the usual definition of adjoints, fixing broken link in the references, etc) in relative adjoint functor.

- Discussion Type
- discussion topicdouble category of algebras
- Category Latest Changes
- Started by Mike Shulman
- Comments 4
- Last comment by varkor
- Last Active Aug 6th 2024

New page: double category of algebras.

- Discussion Type
- discussion topiccohomotopy
- Category Latest Changes
- Started by Urs
- Comments 45
- Last comment by perezl.alonso
- Last Active Aug 6th 2024

At the old entry

*cohomotopy*used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.(We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

- Discussion Type
- discussion topicfibration of quasi-categories
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Hurkyl
- Last Active Aug 6th 2024

am starting fibrations of quasi-categories

- Discussion Type
- discussion topicspherical function
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 6th 2024

- Discussion Type
- discussion topicmapping class group
- Category Latest Changes
- Started by perezl.alonso
- Comments 1
- Last comment by perezl.alonso
- Last Active Aug 6th 2024

Is there a particular reference where these (or rather, their super analogs) are computed for super Riemann surfaces?

- Discussion Type
- discussion topicspatial locale
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 17
- Last comment by Dmitri Pavlov
- Last Active Aug 5th 2024

- Discussion Type
- discussion topicsemidirect product group
- Category Latest Changes
- Started by nLab edit announcer
- Comments 11
- Last comment by nLab edit announcer
- Last Active Aug 5th 2024

- Discussion Type
- discussion topicinequality space
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 5th 2024

- Discussion Type
- discussion topicmodular theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Tom Mainiero
- Last Active Aug 5th 2024

- Discussion Type
- discussion topicenveloping von Neumann algebra
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Tom Mainiero
- Last Active Aug 4th 2024

- Discussion Type
- discussion topicprealgebra real number
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 4th 2024

- Discussion Type
- discussion topicepimorphism
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Aug 4th 2024

felt like adding a handful of basic properties to epimorphism

- Discussion Type
- discussion topicSurj
- Category Latest Changes
- Started by David_Corfield
- Comments 8
- Last comment by varkor
- Last Active Aug 4th 2024

- Discussion Type
- discussion topicDirac manifold
- Category Latest Changes
- Started by perezl.alonso
- Comments 1
- Last comment by perezl.alonso
- Last Active Aug 4th 2024

pointer

- Saskia Demulder, Thomas Raml.
*Poisson-Lie T-duality defects and target space fusion*(2022). (arXiv:2208.04662).

- Saskia Demulder, Thomas Raml.

- Discussion Type
- discussion topicconformal invariance and scale invariance
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Aug 3rd 2024

added pointer to:

- Martin Lüscher, Gerhard Mack:
*Global Conformal Invariance in Quantum Field Theory*, Comm. Math. Phys.**41**3 (1975) 203-234 [doi:10.1007/BF01608988, jstor:cmp/1103898909, inspire:90687]

- Martin Lüscher, Gerhard Mack:

- Discussion Type
- discussion topicdistributivity pullback
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by varkor
- Last Active Aug 3rd 2024

- Discussion Type
- discussion topiclocally cartesian closed category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 5
- Last comment by nLab edit announcer
- Last Active Aug 3rd 2024

In locally cartesian closed category, I wrote out an explicit proof that pullback functors $f^\ast \colon C/Y \to C/X$ between slices preserve exponentials (so that Frobenius reciprocity is satisfied).

- Discussion Type
- discussion topicD-brane
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by perezl.alonso
- Last Active Aug 3rd 2024

- Discussion Type
- discussion topicfactorization algebra
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by zskoda
- Last Active Aug 2nd 2024

added the full definition to factorization algebra

- Discussion Type
- discussion topicfull image
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by J-B Vienney
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicAskey-Wilson polynomial
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

We already have main references at Richard Askey, so why not ?

- Discussion Type
- discussion topicRichard Askey
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicGeorge Andrews
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicYasuhiko Yamada
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Aug 2nd 2024

brief

`category:people`

-entry for hyperlinking references at*elliptic genus*

- Discussion Type
- discussion topicRobinson-Schensted-Knuth correspondence
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicMacdonald Constant-Term Conjecture
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

Not to confuse with Macdonald conjecture on plane partitions.

- Discussion Type
- discussion topicMacdonald conjecture on plane partitions
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicfunctor with smash products
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Aug 2nd 2024

started a minimum at

*functor with smash products*(the realization of ring spectra in terms of lax monoidal functors)In the end this is entirely a story about monoids with respect to Day convolution tensor products. I suppose there is room to say this yet a bit more general abstractly than MMSS00 did.

- Discussion Type
- discussion topicDavid P. Robbins
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicdendroidal set
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by nLab edit announcer
- Last Active Aug 2nd 2024

added at dendroidal set

a section on the relation to simplicial sets

a section on the symmetric monoidal structure on the cat of dendroidal sets

(also added a stubby "overview" section to model structure on dendroidal sets)

- Discussion Type
- discussion topicoctahedron recurrence
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topiclax monoidal category
- Category Latest Changes
- Started by Mike Shulman
- Comments 19
- Last comment by varkor
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicGleb Koshevoy
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicDavid Speyer
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 2nd 2024

- Discussion Type
- discussion topicLawvere-Tierney topology
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by nLab edit announcer
- Last Active Aug 1st 2024

I have expanded Lawvere-Tierney topology, also reorganized it in the process

- Discussion Type
- discussion topicfree coproduct completion
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by varkor
- Last Active Aug 1st 2024

some bare minimum on the free coproduct cocompletion.

The term used to redirect to the entry

*free cartesian category*, where however the simple idea of free coproduct completion wasn’t really brought out.

- Discussion Type
- discussion topiclocally presentable category
- Category Latest Changes
- Started by Tobias Fritz
- Comments 20
- Last comment by qschroed
- Last Active Aug 1st 2024

- 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 topicMartin Lüscher
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 31st 2024

- Discussion Type
- discussion topicRobert Lee Wilson
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jul 31st 2024

Person entry.

Warning: we have a webpage for another algebraist, the group theorist Robert A. Wilson, and elsewhere in the $n$Lab Robert Wilson shortcut is carelessly used for the latter. People tend to shorten links in $n$Lab and the confusion and illegal links might occur in this case. Maybe we should not use version without middle initial for these two guys in links.

- Discussion Type
- discussion topicPhilippe Di Francesco
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jul 31st 2024

- Discussion Type
- discussion topicDodgson condensation
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Jul 31st 2024

In statu nascendi.

A method for calculating determinants. It is related to cluster algebras and a special case of Sylvester identity.

- Discussion Type
- discussion topicmatroid
- Category Latest Changes
- Started by Todd_Trimble
- Comments 22
- Last comment by varkor
- Last Active Jul 31st 2024

I have been adding some material to matroid. I haven’t gotten around to defining oriented matroid yet (and of course there’s much besides to add).

- Discussion Type
- discussion topicBoolean algebra
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by J-B Vienney
- Last Active Jul 31st 2024

Added more material to Boolean algebra, particularly the principle of duality and the connection to Boolean rings, and a wee bit of material on Stone duality.

Stone duality deserves greater expansion, bringing out the dualities via ambimorphic (ahem, schizophrenic) structures on the 2-element set, and mentioning the connection to Chu spaces. Another day, another dollar.

- Discussion Type
- discussion topicglobal equivariant homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by nLab edit announcer
- Last Active Jul 30th 2024

I should say – for those watching the logs and wondering – that I started editing the entry

*global equivariant homotopy theory*such as to reflect Charles Rezk’s account in a coherent way.But I am not done yet. The entry has now some of the key basics, but is still missing the general statement in its relation to orbispaces. Also some harmonizing of the whole entry may be necessary now, as I moved around some stuff.

So better don’t look at it yet. I hope to bring it into shape tomorrow or so.

(In the process I have split off

*global orbit category*now.)

- Discussion Type
- discussion topiccoefficient system
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicG-∞-category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by nLab edit announcer
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicindexed tensor product
- Category Latest Changes
- Started by nLab edit announcer
- Comments 0
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicAaron Naber
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicMichael T. Anderson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicRicci curvature
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 7
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicgraded monad
- Category Latest Changes
- Started by David_Corfield
- Comments 24
- Last comment by varkor
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicStephen Hawking
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicPenrose singularity theorem
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Jul 30th 2024

created a minimum at

*Penrose-Hawking singularity theorem*

- Discussion Type
- discussion topicHawking radiation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicGabriel Wong
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicPranjal Nayak
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 30th 2024

- Discussion Type
- discussion topicD=3 quantum gravity
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Urs
- Last Active Jul 30th 2024

I have expanded the Idea-section at 3d quantum gravity and reorganized the remaining material slightly.

I feel unsure about the pointer to “group field theory” in the References. Can anyone list results that have come out of group field theory that are relevant here?

I find the following noteworthy, and I am not sure if this is widely appreciated:

the original discussion of the quantization of 3d gravity by Witten in 1988 happens work out to be precisely along the lines that “loop quantum gravity” once set out to get to work in higher dimensions: one realizes

that the configuration space is equivalently a space of connections;

that these can be characterized by their parallel transport along paths in base space;

that therefore observables of the theory are given by evaluating on choices of paths (an idea that goes by the unfortunate name “spin network”).

All this is in Witten’s 1988 article. Of course the point there is that in the case of 3d this can actually be made to work. The reason is that in this case it is sufficient to restrict to

*flat*connections and for these everything drastically simplifies: their parallel transport depends not on the actual paths but just on their homotopy class, rel boundary. Accordingly the “spin networks” reduce to evaluations on generators of the fundamental group, etc.Notice that in 4d the analog of this step that Witten easily performs in 3d was never carried out: instead, because it seemed to hard, the LQG literature

*always*passes to a different system, where smooth connections are replaced by parallel transport that is required to be neigher smooth nor in fact continuous. These are called “generalized connections” in the LQG literature. Of course these have nothing much to do with Einstein-gravity: because there the configuration space does not contain such “generalized” fields.For these reasons I feel a bit uneasy when the entry refers to LQG or spin foams as “other approaches” to discuss 3d quantum gravity. First of all, the existing good discussion by Witten did realize the LQG idea already in that dimension, and it did it correctly. So in which sense are there “other approaches”?

Which insights on 3d quantum gravity do “spin foam”s or does “group field theory”add? If anyone could list some results with concrete pointers to the literature, I’d be most grateful.