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- Discussion Type
- discussion topicshift
- Category Latest Changes
- Started by PaoloPerrone
- Comments 1
- Last comment by PaoloPerrone
- Last Active Jul 21st 2024

- Discussion Type
- discussion topictail event
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by PaoloPerrone
- Last Active Jul 21st 2024

- Discussion Type
- discussion topicSandbox
- Category Latest Changes
- Started by Andrew Stacey
- Comments 5
- Last comment by Daniel Geisler
- Last Active Jul 21st 2024

Actually, taking a look at the Sandbox, it's a bit full up and could do with a clean out (I shan't comment on what one usually finds in sandboxes in children's playgrounds ...). I propose we copy any serious words of wisdom to the HowTo, blank the Sandbox, and replace with a link to its own history.

I know, I know, it's a wiki so I ought to just do it, but I figured that this was something I should get some consensus on first to see if it's just me that doesn't like it.

- Discussion Type
- discussion topicNicolae Popescu
- Category Latest Changes
- Started by RodMcGuire
- Comments 1
- Last comment by RodMcGuire
- Last Active Jul 21st 2024

rescued planetmath link and added Wiki link

planetmath: Nicolae Popescu (mathematician) Broken Internet Archive

Wikipedia: Nicolae Popescu

- Discussion Type
- discussion topicadditive and abelian categories
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by ncfavier
- Last Active Jul 21st 2024

- Discussion Type
- discussion topicnon-canonical isomorphism
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by ncfavier
- Last Active Jul 21st 2024

- Discussion Type
- discussion topicJin-Cheng Guu
- Category Latest Changes
- Started by jin
- Comments 2
- Last comment by jin
- Last Active Jul 20th 2024

- Discussion Type
- discussion topicconformal field theory
- Category Latest Changes
- Started by Tim_van_Beek
- Comments 43
- Last comment by jin
- Last Active Jul 20th 2024

I began to add a definition of conformal field theory using the Wightman resp. Osterwalder-Schrader axiomatic approach. My intention is to define and explain the most common concepts that appear again and again in the physics literature, but are rarely defined, like “primary field” or “operator product expansion”.

(I remember that I asked myself, when I first saw an operator product expansion, if the existence of one is an axiom or a theorem, I don’t remember reading or hearing an answer of that until I looked in the book by Schottenloher).

- Discussion Type
- discussion topicDrinfel'd double
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by zskoda
- Last Active Jul 20th 2024

I gave

*Drinfel’d double*an Idea-section.Also moved a paragraph on module categories from the References to a Properties-section.

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 55
- Last comment by varkor
- Last Active Jul 20th 2024

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 topicLawvere interval
- Category Latest Changes
- Started by jonsterling
- Comments 18
- Last comment by Hurkyl
- Last Active Jul 20th 2024

- Discussion Type
- discussion topicKenneth Brown
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Jul 19th 2024

Erased the reference of Edgar Brown which is misplaced here in version 9.

P.S. The link to Brown’s webpage does not seem to work.

- Discussion Type
- discussion topicmonad
- Category Latest Changes
- Started by Urs
- Comments 102
- Last comment by zskoda
- Last Active Jul 19th 2024

following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

- Discussion Type
- discussion topiclifting a function
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Jul 19th 2024

- Discussion Type
- discussion topicfinal functor
- Category Latest Changes
- Started by Tom Hirschowitz
- Comments 20
- Last comment by varkor
- Last Active Jul 19th 2024

- Discussion Type
- discussion topicWu manifold
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 5
- Last comment by Samuel Adrian Antz
- Last Active Jul 19th 2024

Created stub for Wu manifold, which is now linked on rational homology sphere.

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 110
- Last comment by John Baez
- Last Active Jul 19th 2024

Todd,

when you see this here and have a minute, would you mind having a look at

*monoidal category*to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?Thanks!

- Discussion Type
- discussion topicenhanced factorisation system
- Category Latest Changes
- Started by varkor
- Comments 6
- Last comment by varkor
- Last Active Jul 19th 2024

- Discussion Type
- discussion topicweight systems on chord diagrams in physics
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active Jul 19th 2024

- Discussion Type
- discussion topicAb-enriched category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Urs
- Last Active Jul 19th 2024

- Discussion Type
- discussion topicPo-Hsiang Chu
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicpost-Lie algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jul 18th 2024

Stub, for now just to record relevant references. Related to the recently added entry Magnus expansion and also to pre-Lie algebra.

- Discussion Type
- discussion topicViviane Pons
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

category: people page for the reference

- Viviane Pons,
*Combinatorics of the Permutahedra, Associahedra, and Friends*(arXiv:2310.12687)

Anonymouse

- Viviane Pons,

- Discussion Type
- discussion topicassociahedron
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron

- Discussion Type
- discussion topicpermutahedron
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topictrefoil knot
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicframed link
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Urs
- Last Active Jul 18th 2024

I tried adding some material to framed link, but as in other recent edits (Dehn twist, Dehn surgery), my efforts might well make an expert smile indulgently. I do mean to – or someone else could – fix up or polish up the recent edit at Dehn surgery, which I’m not particularly happy with at the moment.

- Discussion Type
- discussion topicHenri Lombardi
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicAssia Mahboubi
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicuniversal algebra
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicsynthetic domain theory
- Category Latest Changes
- Started by maxsnew
- Comments 9
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicstar-polycategory
- Category Latest Changes
- Started by Sam Staton
- Comments 10
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

After this discussion at string diagrams for linearly distributive categories with unit = counit, I finally got round to having a go at making star-polycategory. Still much more to do. Hopefully I didn’t make any major mistakes so far.

- Discussion Type
- discussion topicrealizability
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

we were lacking an entry

*realizability*that points to all the related entries (and in fact some entries were asking for just “realizability”).So I started one. Put in the following Idea-paragraph:

The idea of

*realizability*is essentially that of constructivism, intuitionistic mathematics and the propositions as types paradigm: for instance constructively a proof of an existential quantification $\underset{x\in X}{\exists} \phi(x)$ consists of constructing a specific $x \in X$ and a proof of $\phi(x)$, which “realizes” the truth of the statement, whence the name (e.g. Vermeeren 09, section 1).

- Discussion Type
- discussion topicreal numbers object
- Category Latest Changes
- Started by Corbin
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

Clean up a couple parenthetical remarks. The page ring object seems to indeed have the desired diagrams.

- Discussion Type
- discussion topicpropositional axiom of choice
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

a stub, just to finally make the link work (which has been requested for ages at

*inhabited set*,*dominance*and*inhabited object*)

- Discussion Type
- discussion topicproof theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

I have made some trivial edits to the wording, hoping to make it flow more nicely.

By the way, this entry is linking (at least now that I adjusted the plural redirect) to

*recursive function*. This is only natural, but – unfortunately – our entry*recursive function*is empty (and always has been)!Much of the material needed there is at

*partial recursive function*. We should either put redirects or (better) add a little bit of content to*recursive function*.

- Discussion Type
- discussion topicmonad transformer
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

I have added (here) pointer to:

- Sergei Winitzki, Chapter 14 of:
*The Science of Functional Programming – A tutorial, with examples in Scala*(leanpub:sofp)

(This edit prompted by discussion in another thread of the same name: here)

- Sergei Winitzki, Chapter 14 of:

- Discussion Type
- discussion topicmonad (in computer science)
- Category Latest Changes
- Started by Urs
- Comments 46
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicinternal subcategory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicgame semantics
- Category Latest Changes
- Started by David_Corfield
- Comments 8
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

I was going to start game semantics to record a couple of references to dependent type theory, but I’m getting an error message at the moment. So I’ll just leave here for now:

## Idea

In logic,

**game semantics**is used to provide a semantic interpretation of logic constructions in terms of strategies for opposing players to win a game corresponding to some proposition.## References

- Wilfred Hodges, 2013,
*Logic and Games*, (SEP)

For attempts to formulate a game semantics for dependent type theory, see

Matthijs Vakar, Radha Jagadeesan, Samson Abramsky,

*Game Semantics for Dependent Types*, (pdf)Norihiro Yamada, _Game Semantics for Martin-Löf Type Theory, (arXiv:1610.01669)

- Wilfred Hodges, 2013,

- Discussion Type
- discussion topicfilter space
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicfan theorem
- Category Latest Changes
- Started by MarkSaving
- Comments 6
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

Change 1: Original page describes the fan theorem as requiring the bar to be decidable, claims that the “classical” fan theorem contradicts Brouwer’s continuity principle. The latter claim is not true; I corrected the error. I have stated the result as two separate theorems: the decidable fan theorem, about decidable bars, and the fan theorem, about bars in general.

Change 2: Slightly more information is provided about the relationship between the Fan Theorem and Bar Induction. Eventually, we should make a page about the latter.

Change 3: the section on equivalents to the fan theorem has been fixed somewhat. The section originally asserted that all of the statements provided were equivalent to the decidable fan theorem; in fact, some are equivalent to the decidable fan theorem and some to the full fan theorem.

- Discussion Type
- discussion topiccomplete small category
- Category Latest Changes
- Started by Mike Shulman
- Comments 16
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

Created complete small category, and moved the proof of Freyd’s theorem to there from adjoint functor theorem.

- Discussion Type
- discussion topiccategorical algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

Edited the text in the Idea-section, such as to make the terms

*monoidal category*,*monoid objects*,*module objects*appear.

- Discussion Type
- discussion topiccalculus of constructions
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

I have added the following paragraph to

*calculus of constructions*, I’d be grateful if experts could briefly give me a sanity check that this is an accurate characterization:More in detail, the

*Calculus of (co)Inductive Constructions*isa system of natural deduction with dependent types;

with the natural-deduction rules for dependent product types specified;

and with a rule for how to introduce new such natural-deduction rules for arbitrary (co)inductive types.

and with a type of types (hierarchy).

- Discussion Type
- discussion topicJohn Power
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

I fixed a strange link at John Power.

- Discussion Type
- discussion topicMartin Hyland
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicYiannis Vlassopoulos
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by zskoda
- Last Active Jul 18th 2024

Expanded the entry by more references.

I have erased two redirects which used to be (probably) in Greek but some $n$Lab upgrade has obliterated the difference between the characters and now it was ????? or alike and the info is lost. If somebody has his Greek spelling can ressurect the redirects. I have now changed the page name to his arXiv spelling and put Ioannis Vlassopoulos as a redirect.

- Discussion Type
- discussion topicwreath product of groups
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicinhomogeneous cosmology
- Category Latest Changes
- Started by Urs
- Comments 45
- Last comment by Urs
- Last Active Jul 18th 2024

started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective

- Discussion Type
- discussion topicAndreas Schmitt
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicNicolas Kovensky
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicAdS-QCD correspondence
- Category Latest Changes
- Started by Urs
- Comments 96
- Last comment by Urs
- Last Active Jul 18th 2024

- Discussion Type
- discussion topiczero-one law
- Category Latest Changes
- Started by PaoloPerrone
- Comments 4
- Last comment by PaoloPerrone
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicmodel structure on diffeological spaces
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 18th 2024

a stub entry, for the moment just so as to give a home to these two references:

Hiroshi Kihara,

*Model category of diffeological spaces*, Journal of Homotopy and Related Structures, (2018), 1-40 (arXiv:1605.06794)Tadayuki Haraguchi, Kazuhisa Shimakawa,

*A model structure on the category of diffeological spaces*(arXiv:1311.5668)

- Discussion Type
- discussion topicwreath product of wreaths
- Category Latest Changes
- Started by mattecapu
- Comments 1
- Last comment by mattecapu
- Last Active Jul 18th 2024

- Discussion Type
- discussion topiclinking number
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 18th 2024

added pointer to:

- Renzo Ricca, Bernardo Nipoti:
*Gauss’ Linking Number Revisited*, Journal of Knot Theory and Its Ramifications**20**10 (2011) 1325-1343 [doi:10.1142/S0218216511009261, pdf]

- Renzo Ricca, Bernardo Nipoti:

- Discussion Type
- discussion topicwreath product
- Category Latest Changes
- Started by mattecapu
- Comments 1
- Last comment by mattecapu
- Last Active Jul 18th 2024

- Discussion Type
- discussion topicempty 223
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 18th 2024

added this second-order-quote:

Chen Ning Yang writes in

*C. N. Yang, Selected papers, 1945-1980, with commentary*, W. H. Freeman and Company, San Francisco, 1983, on p. 567:In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

- Discussion Type
- discussion topicempty 222
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2024