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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topicmutually unbiased bases
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicgeneral relativity
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 7th 2023

I wanted to be able to use the link without it appearing in grey, so I created a stub for general relativity.

- Discussion Type
- discussion topicstar-autonomous category
- Category Latest Changes
- Started by Mike Shulman
- Comments 30
- Last comment by Mike Shulman
- Last Active Mar 7th 2023

I added to star-autonomous category a mention of “$\ast$-autonomous functors”.

- Discussion Type
- discussion topicPauli gate
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicZX-calculus
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicElham Kashefi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicVincent Danos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicmeasurement-based quantum computation
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicMaarten Van den Nest
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicWolfgang Dür
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicDan E. Browne
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicDebbie W. Leung
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicHans J. Briegel
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicRobert Raussendorf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicGerard J. Milburn
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicSimon Perdrix
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicMike Shulman
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Guest
- Last Active Mar 7th 2023

Added

- Mike Shulman,
*Semantics of multimodal adjoint type theory*(arXiv:2303.02572)

the first now of ’Selected writings’.

- Mike Shulman,

- Discussion Type
- discussion topicquantum reader monad
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 7th 2023

now creating this entry.

The technical material under “Details” (here) is copied over from what I had written at

*reader monad – Examples – quantum reader monad*. (There may still be room left to adjust the wording in order to reflect that this material moved to a new entry.)To this I have now added an Idea-section (here) which highlights the relation to (equivalence with) Bob Coecke’s “classical structures” (which term I made redirect to here now)

- Discussion Type
- discussion topicEuler characteristic
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by David_Corfield
- Last Active Mar 7th 2023

In order to accompany the nCafe discussion I have started to add some content to the entry Euler characteristic

- Discussion Type
- discussion topicShou-Cheng Zhang
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 7th 2023

brief

`category:people`

-entry for hyperlinking references at*quantum spin Hall effect*

- Discussion Type
- discussion topicsemi-metal
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicStefano Gogioso
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicquantum information theory via string diagrams -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 7th 2023

splitting off and expanding this list of references from

*quantum information theory via dagger-compact categories*, to be re-`!include`

d there and elsewhere, for ease of syncing

- Discussion Type
- discussion topicmodal type theory
- Category Latest Changes
- Started by Urs
- Comments 98
- Last comment by David_Corfield
- Last Active Mar 7th 2023

created an entry

*modal type theory*; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with*monad (in computer science)*.

- Discussion Type
- discussion topicFarzan Vafa
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicBiao Lian
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicanyonic braiding in momentum space -- references
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 7th 2023

a bare list of references, to be

`!include`

-ed into the References-section of relevant entries (such as at*braid group representation*and at*semi-metal*).Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited

- Discussion Type
- discussion topicDaniel Thomas
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicAli Mozaffari
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicEanna Flanagan
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by Urs
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicBertrand Russell
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active Mar 7th 2023

added (here) pointer to Russell’s 1922 speech

*Free Thought and Official Propaganda*, with some quotes

- Discussion Type
- discussion topicMOND
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Guest
- Last Active Mar 7th 2023

recorded some recent surveys of the status of MOND at

*MOND*

- Discussion Type
- discussion topicTom Zlosnik
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Guest
- Last Active Mar 7th 2023

- Discussion Type
- discussion topicMordehai Milgrom
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active Mar 7th 2023

Added selected writings section and reference

- Mordehai Milgrom,
*Broader view of bimetric MOND*, Physical Review D, Volume 106, Issue 8. Published 10 October 2022. (doi:10.1103/PhysRevD.106.084010, arXiv:2208.10882)

- Mordehai Milgrom,

- Discussion Type
- discussion topiccopairing
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Mar 6th 2023

- Discussion Type
- discussion topiccodiagonal
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by DavidRoberts
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicextensive category
- Category Latest Changes
- Started by Sam Staton
- Comments 43
- Last comment by DavidRoberts
- Last Active Mar 6th 2023

In the examples section of extensive category, it is stated that the category of affine schemes is infinitary extensive.

For all I know, I was the one who stuck in that example. But is that statement actually true? I’m having trouble seeing it.

If $S$ is a commutative ring over $R$ (by which I mean under $R$ (-:), does the functor $S \otimes_R -: CAlg_R \to CAlg_R$ preserve arbitrary cartesian products? Because it seems that’s what we basically need for the statement to be true.

- Discussion Type
- discussion topicsmash product type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicbraid cobordism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicPROP
- Category Latest Changes
- Started by fpaugam
- Comments 32
- Last comment by BryceClarke
- Last Active Mar 6th 2023

- I would like to include something on wheeled properads (or wheeled PROPs) in the nlab. It seems to me that a wheeled prop is something like a symmetric monoidal category with duals for every object generated by one object. Is this right? Is there a place in the litterature where i can find the relation between wheeled properads used by Merkulov and some kinds of symmetric monoidal categories with duality?

Before changing the PROP entry to add this variant, i would like to have a nice reference on this.

- Discussion Type
- discussion topiccertified programming
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Urs
- Last Active Mar 6th 2023

I created a stub

*certified programming*.That’s motivated from me having expanded the Idea-section at

*type theory*. I enjoyed writing the words “is used in industry”. There are not many $n$Lab pages where I can write these words.I am saying this only half-jokingly. Somehow there is something deep going on.

Anyway, in (the maybe unlikely) case that somebody reading this here has lots of information about the use and relevance of certified programming in industry, I’d enjoy seeing more information added to that entry.

- Discussion Type
- discussion topicConner-Floyd isomorphism
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 6th 2023

I have expanded out the statement of (the ingredients of) the isomorphism a bit more and made explicit the statement of the relation to the Landweber exact functor theorem.

- Discussion Type
- discussion topicMarc Hoyois
- Category Latest Changes
- Started by Marc Hoyois
- Comments 3
- Last comment by Urs
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicalgebraic cobordism
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active Mar 6th 2023

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 topicW-type
- Category Latest Changes
- Started by Mike Shulman
- Comments 25
- Last comment by DavidRoberts
- Last Active Mar 6th 2023

Created W-type.

- Discussion Type
- discussion topicunivalence axiom
- Category Latest Changes
- Started by spitters
- Comments 43
- Last comment by rbocquet
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicAlex Kavvos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 6th 2023

- Discussion Type
- discussion topicdirected homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Mar 6th 2023

created directed homotopy type theory

- Discussion Type
- discussion topicorbifold
- Category Latest Changes
- Started by Urs
- Comments 47
- Last comment by Urs
- Last Active Mar 6th 2023

I am moving the following old query box exchange from orbifold to here.

old query box discussion:

I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely

**does not**view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?

Urs Schreiber: please, go ahead. It would be appreciated.

end of old query box discussion

- Discussion Type
- discussion topiccategory theory
- Category Latest Changes
- Started by Eric
- Comments 80
- Last comment by Urs
- Last Active Mar 5th 2023

I removed some spam on category theory.

- Discussion Type
- discussion topicHans Freudenthal
- Category Latest Changes
- Started by Thomas Holder
- Comments 2
- Last comment by Urs
- Last Active Mar 5th 2023

- Discussion Type
- discussion topicdirected type theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 5th 2023

a brief

`category:disambigation`

-page, for the moment just to ensure that the reader of*2-type theory*will find an unbroken link for*directed type theory*which will alert them of the existence of*directed homotopy type theory*

- Discussion Type
- discussion topicmathematical statements --- contents
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 5th 2023

I am finally creating this entry — meant as a bare list of hyperlinked terms to be

`!include`

-ed into the “Related concepts”-sections of the respective entries — for ease of synchronizing this list across all these entries.(I am not sold on the title “mathematical statements”, it’s just the best I could come up with after a minute of thinking about it).

I am creating this now with the following list, but this may change as I now go through all the related entries:

- Discussion Type
- discussion topicconjecture
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 5th 2023

Added an Idea-section to this (previously stubby) entry — not meant to be definite, just what came to mind when finding that such a section was still lacking here:

In mathematics, a

*conjecture*is a proposition which is*expected*to be true, hence expected to have a proof, but for which no proof is (currently) known.Hence being a conjecture is a sociological aspect of a proposition, not a mathematical aspect: Once a proof (or else a counterexample) is found, the conjecture ceases to be a conjecture and instead becomes a theorem.

It happens that conjectures remain unproven while being perceived as trustworthy enough that further theorems are proven

*assuming*the conjectures – in this case the conjecture plays the role of a hypothesis in the sense of formal logic.For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).

In other cases the term “hypothesis” is used synonymously with “conjecture” – e.g. for the

*homotopy hypothesis*(key cases of which have long become theorems) or the*cobordism hypothesis*(on which a proof has famously been claimed but not universally accepted).

- Discussion Type
- discussion topichypothesis
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 5th 2023

cross-linked with

*conjecture*, adding these lines (following after the paragraph that starts out with “In formal logic…”):In the practice of mathematics (or beyond), hypotheses that that are

*expected*to have a proof, even if currently unknown, are known as*conjectures*.For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).

- Discussion Type
- discussion topicdomain theory
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Ulrik
- Last Active Mar 5th 2023

added pointer to:

- Tom de Jong, Martín Hötzel Escardó,
*Domain Theory in Constructive and Predicative Univalent Foundations*, in:*29th EACSL Annual Conference on Computer Science Logic*, CSL 2021, LIPIcs proceedings 183, 2021 (doi:10.4230/LIPIcs.CSL.2021.28, arXiv:2008.01422)

- Tom de Jong, Martín Hötzel Escardó,

- Discussion Type
- discussion topicfunctoriality of categories of presheaves
- Category Latest Changes
- Started by anuyts
- Comments 6
- Last comment by anuyts
- Last Active Mar 5th 2023

- Discussion Type
- discussion topicinfinitesimal object
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active Mar 5th 2023

added a section Spaces of infinitesimal simplices

- Discussion Type
- discussion topicflux
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 5th 2023

one possible bit of information at flux

- Discussion Type
- discussion topicflux quantization in superconductors -- section
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 5th 2023

this is a bare section, meant to be

`!include`

-ed into relevant entries (such as at*superconductor*,*vortex*,*Dirac charge quantization*and maybe elsewhere) as mentioned here