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- Discussion Type
- discussion topicinertia orbifold
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by David_Corfield
- Last Active Apr 30th 2024

- Discussion Type
- discussion topicGermán Sierra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 30th 2024

- Discussion Type
- discussion topicMoustafa A. Awada
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 30th 2024

- Discussion Type
- discussion topiccotorsion pair
- Category Latest Changes
- Started by perezl.alonso
- Comments 1
- Last comment by perezl.alonso
- Last Active Apr 30th 2024

pointer

- Huimin Chang, Panyue Zhou.
*Mutation of n-cotorsion pairs in triangulated categories*(2024). (arXiv:2404.18336).

- Huimin Chang, Panyue Zhou.

- Discussion Type
- discussion topicbraided monoidal functor
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by mattecapu
- Last Active Apr 30th 2024

created stub for braided monoidal functor – but still too lazy to type the diagrams in the axioms

- Discussion Type
- discussion topic(n,r)-category
- Category Latest Changes
- Started by Guest
- Comments 22
- Last comment by Mike Shulman
- Last Active Apr 30th 2024

- Comment at (n,r)-category about the equivalence of fundamental categories. This is a coarser notion than equivalence of categories in the usual sense.

-David Roberts

- Discussion Type
- discussion topicenriched groupoid
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Mike Shulman
- Last Active Apr 30th 2024

- Discussion Type
- discussion topicempty type
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Mike Shulman
- Last Active Apr 30th 2024

- Discussion Type
- discussion topicorbital ∞-category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Apr 29th 2024

- Discussion Type
- discussion topicwreath
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active Apr 29th 2024

- Discussion Type
- discussion topicKeith J. Bauer
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 29th 2024

- Discussion Type
- discussion topiccancellative midpoint algebra
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by Urs
- Last Active Apr 29th 2024

- Discussion Type
- discussion topicSerre's theorem on Proj
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Dmitri Pavlov
- Last Active Apr 28th 2024

- Discussion Type
- discussion topicZbigniew Fiedorowicz
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 28th 2024

- Discussion Type
- discussion topicsequential multicategory
- Category Latest Changes
- Started by varkor
- Comments 2
- Last comment by varkor
- Last Active Apr 28th 2024

- Discussion Type
- discussion topicidempotent monad
- Category Latest Changes
- Started by Todd_Trimble
- Comments 13
- Last comment by zskoda
- Last Active Apr 28th 2024

I added more to idempotent monad, in particular fixing a mistake that had been on there a long time (on the associated idempotent monad). I had wanted to give an example that addresses Mike’s query box at the bottom, but before going further, I wanted to track down the reference of Joyal-Tierney, or perhaps have someone like Zoran fill in some material on classical descent theory for commutative algebras (he wrote an MO answer about this once) to illustrate the associated idempotent monad.

Some of this (condition 2 in the proposition in the section on algebras) was written as a preparatory step for a to-be-written nLab article on Day’s reflection theorem for symmetric monoidal closed categories, which came up in email with Harry and Ross Street.

- Discussion Type
- discussion topicLie-Rinehart pair
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Praphulla
- Last Active Apr 28th 2024

- created Lie-Rinehart pair

- Discussion Type
- discussion topicPaul Bernays
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 28th 2024

- Discussion Type
- discussion topicFreund-Rubin compactification
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 27th 2024

- Discussion Type
- discussion topicD=11 N=1 supergravity
- Category Latest Changes
- Started by David_Corfield
- Comments 12
- Last comment by Urs
- Last Active Apr 27th 2024

- Discussion Type
- discussion topicgravity
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Apr 27th 2024

added to gravity references discussing the covariant phase space of gravity, as part of a reply to this TP.SE-question

- Discussion Type
- discussion topicdoctrinal adjunction
- Category Latest Changes
- Started by FinnLawler
- Comments 7
- Last comment by mattecapu
- Last Active Apr 27th 2024

Created doctrinal adjunction. The page could probably use some examples and/or fleshing out.

- Discussion Type
- discussion topicGiry monad
- Category Latest Changes
- Started by zskoda
- Comments 64
- Last comment by Urs
- Last Active Apr 27th 2024

Added a reference of Robert Furber, Bart Jacobs at Giry monad.

- Discussion Type
- discussion topicBell's inequality
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 27th 2024

added this:

Relation to (identification with) much older inequalities in classical probability theory, due to George Boole was pointed out by (among others, called the “probabilistic opposition” in Khrennikov 2007, p. 3):

Luigi Accardi,

*The Probabilistic Roots of the Quantum Mechanical Paradoxes*, in:*The Wave-Particle Dualism*, Fundamental Theories of Physics**3**Springer (1984) [doi:10.1007/978-94-009-6286-6_16Itamar Pitowsky,

*From George Boole To John Bell — The Origins of Bell’s Inequality*, in:*Bell’s Theorem, Quantum Theory and Conceptions of the Universe*, Fundamental Theories of Physics**37**Springer (1989) [doi:10.1007/978-94-017-0849-4_6]

reviewed in

Elemer E Rosinger,

*George Boole and the Bell inequalities*[arXiv:quant-ph/0406004]{#Khrennikov07} Andrei Khrennikov,

*Bell’s inequality: Physics meets Probability*[arXiv:0709.3909]Andrei Khrennikov,

*Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?*, Entropy**10**2 (2008) 19-32 [doi:10.3390/entropy-e10020019]

- Discussion Type
- discussion topicGelfand-type duality for commutative von Neumann algebras
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Apr 26th 2024

Created:

## Idea

An analogue of the Gelfand duality for commutative von Neumann algebras.

## Statement

The following five categories are equivalent.

The opposite category of commutative von Neumann algebras and normal *-homomorphisms.

The category of measurable locales, which is a full subcategory of the category of locales.

The category of hyperstonean locales and open maps of locales.

The category of hyperstonean spaces and open continuous maps.

The category of compact strictly localizable enhanced measurable spaces and equivalence classes of measurable negligibility-reflecting maps modulo the equivalence relation of weak equality almost everywhere.

## Reference

- Dmitri Pavlov,
*Gelfand-type duality for commutative von Neumann algebras*, Journal of Pure and Applied Algebra 226:4 (2022), 106884, 1–53. doi:10.1016/j.jpaa.2021.106884, arXiv.

- Discussion Type
- discussion topicSonia Stanciu
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 26th 2024

- Discussion Type
- discussion topicDirac charge quantization
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 26th 2024

- Discussion Type
- discussion topicorthosymplectic super Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Apr 26th 2024

have started something at

*orthosymplectic super Lie algebra*and have added little bits and pieces to various related entries, such as first sketchy notes at*super Lie algebra – classification*and at*supersymmetry – Classification – superconformal symmetry*.Nothing of this is done yet, but I need to call it quits now.

- Discussion Type
- discussion topicVladimir Rittenberg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 26th 2024

- Discussion Type
- discussion topicsuper Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Apr 26th 2024

added a few references and links to super Lie algebra

- Discussion Type
- discussion topicpara-quaternionic structure
- Category Latest Changes
- Started by perezl.alonso
- Comments 3
- Last comment by perezl.alonso
- Last Active Apr 26th 2024

- Discussion Type
- discussion topiccyclic group
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 26th 2024

at

*cyclic group*there had been a typo that said “free group” instead of “cyclic group” (in the Examples-section). I have fixed that.Somehow I think this entry could be organized differently, but I won’t do that now.

- Discussion Type
- discussion topicquiver representation
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Apr 26th 2024

I just discovered that, all along, the term “quiver representation” was just redirecting to

*representation*. Have started this dedicated page now, with the bare minimum

- Discussion Type
- discussion topicsimplex category
- Category Latest Changes
- Started by FinnLawler
- Comments 24
- Last comment by nLab edit announcer
- Last Active Apr 26th 2024

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 topicC2-equivariant homotopy groups of spheres
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by nLab edit announcer
- Last Active Apr 25th 2024

- Discussion Type
- discussion topicCalabi-Yau algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Apr 25th 2024

stub for Calabi-Yau algebra

- Discussion Type
- discussion topiccone
- Category Latest Changes
- Started by Eric
- Comments 14
- Last comment by nLab edit announcer
- Last Active Apr 25th 2024

Added a diagram to cone and changed some notation to be compatible with cone morphism and Understanding Constructions in Set

- Discussion Type
- discussion topicdependent linear type theory
- Category Latest Changes
- Started by Urs
- Comments 93
- Last comment by David_Corfield
- Last Active Apr 25th 2024

Following discussion in some other threads, I thought one should make it explicit and so I created an entry

Currently this contains some (hopefully) evident remarks of what “dependent linear type theory” reasonably should be at least, namely a hyperdoctrine with values in linear type theories.

The entry keeps saying “should”. I’d ask readers to please either point to previous proposals for what “linear dependent type theory” is/should be, or criticise or else further expand/refine what hopefully are the obvious definitions.

This is hopefully uncontroversial and should be regarded an obvious triviality. But it seems it might be one of those hidden trivialities which deserve to be highlighted a bit more. I am getting the impression that there is a big story hiding here.

Thanks for whatever input you might have.

- Discussion Type
- discussion topicMoore closure
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by gejza.jenca
- Last Active Apr 25th 2024

edited

*Moore closure*. Added a bit more glue, restructured slightly, and added more hyperlinks.

- Discussion Type
- discussion topicconservative cocompletion
- Category Latest Changes
- Started by varkor
- Comments 6
- Last comment by ʇɐ
- Last Active Apr 25th 2024

- Discussion Type
- discussion topicgroup
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by ʇɐ
- Last Active Apr 25th 2024

reformatted the entry group a little, expanded the Examples-section a little and then pasted in the group-related “counterexamples” from counterexamples in algebra. Mainly to indicate how I think this latter entry should eventually be used to improve the entries that it refers to.

- Discussion Type
- discussion topicJoseph Tooby-Smith
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 25th 2024

- Discussion Type
- discussion topicJJ
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Apr 25th 2024

- Discussion Type
- discussion topiccombinatorial category
- Category Latest Changes
- Started by varkor
- Comments 8
- Last comment by varkor
- Last Active Apr 25th 2024

- Discussion Type
- discussion topicequivariant homotopy group
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Apr 25th 2024

- Discussion Type
- discussion topicHopf link - SVG
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicBorromean link - SVG
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicBastiaan Cnossen
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicSil Linskens
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicTobias Lenz
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicKaif Hilman
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
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- Last Active Apr 24th 2024

- Discussion Type
- discussion topicBert Guillou
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
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- Last Active Apr 24th 2024

- Discussion Type
- discussion topicDaniel Isaksen
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicLorenzo Riva
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicfunctorial field theory
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active Apr 24th 2024

I am beginning to give the entry

*FQFT*a comprehensive*Exposition and Introduction*section.So far I have filled some genuine content into the first subsection

*Quantum mechanics in Schrödinger picture*.But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.

- Discussion Type
- discussion topicsuper anti de Sitter spacetime
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Apr 24th 2024

cross-linked with

*super Klein geometry*

- Discussion Type
- discussion topicHopf algebra
- Category Latest Changes
- Started by Urs
- Comments 36
- Last comment by perezl.alonso
- Last Active Apr 24th 2024

added to the Properties-section at Hopf algebra a brief remark on their interpretation as 3-vector spaces.

- Discussion Type
- discussion topicAlexander Stottmeister
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicquantum embezzlement
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 24th 2024

- Discussion Type
- discussion topicvon Neumann algebra factor
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Apr 24th 2024

stub for von Neumann algebra factor