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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory 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 stack 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 topicShor's algorithm
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicQuipper
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Aug 17th 2023

added pointer to:

- Peng Fu, Kohei Kishida, Neil Ross, Peter Selinger,
*A Tutorial Introduction to Quantum Circuit Programming in Dependently Typed Proto-Quipper*, in I. Lanese, M. Rawski (eds.)*Reversible Computation*RC 2020. Lecture Notes in Computer Science, vol 12227 (arXiv:2005.08396, doi:10.1007/978-3-030-52482-1_9)

- Peng Fu, Kohei Kishida, Neil Ross, Peter Selinger,

- Discussion Type
- discussion topicnonabelian cohomology
- Category Latest Changes
- Started by nLab edit announcer
- Comments 25
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicdynamical system
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicuniversal algebra
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicMichael Johnson
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicMatthew Di Meglio
- Category Latest Changes
- Started by BryceClarke
- Comments 2
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicnon-projected super Riemann surface moduli -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2023

a stand-alone sub-section, to be

`!include`

-ed at*moduli space of super Riemann surfaces*and at*super Riemann surface*, for ease of synchronization

- Discussion Type
- discussion topicsuper-moduli of super Riemann surfaces -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2023

a bare subsection with a list of references, to be

`!include`

-ed at*super Riemann surface*and at*moduli space of super Riemann surfaces*, for ease of synchronization

- Discussion Type
- discussion topicsuper Riemann surface
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Aug 17th 2023

created a stub for

*super Riemann surface*, just to record Witten’s latest

- Discussion Type
- discussion topicNadia Ott
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2023

- Discussion Type
- discussion topicquantum programming languages -- references
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Aug 16th 2023

a bare list of references, to be

`!includ`

-ed into the list of references of relevant entries, such as at*quantum computing*and*quantum programming*, for ease of updating and syncing

- Discussion Type
- discussion topiccertified programming
- Category Latest Changes
- Started by Urs
- Comments 44
- Last comment by Urs
- Last Active Aug 16th 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 topicD. Scott Alexander
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicHarald Weinfurter
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicJohn A. Smolin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicTycho Sleator
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicNorman Margolus
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicAdriano Barenco
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2023

- Discussion Type
- discussion topicquantum logic gate
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Aug 16th 2023

a stub, to make links work

(This used to be a stub “quantum circuit” which I just quasi-duplicated at a more extensive entry

*quantum circuit diagram*. But since*quantum gate*was already redirecting here – which is how I discovered/remembered that this entry exists – no harm is done by making that it’s new title.)

- Discussion Type
- discussion topicquantum gravity
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Aug 16th 2023

in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity

- Discussion Type
- discussion topicaffine Grassmannian
- Category Latest Changes
- Started by Anton Hilado
- Comments 2
- Last comment by Anton Hilado
- Last Active Aug 15th 2023

- Discussion Type
- discussion topicvariable rule
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 15th 2023

An entry of this title had long been requested by various other entries (such as at

*structural rule*).

- Discussion Type
- discussion topicexchange rule
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 15th 2023

added pointer to:

- Bart Jacobs, p. 122 in:
*Categorical Logic and Type Theory*, Studies in Logic and the Foundations of Mathematics**141**, Elsevier (1998) [ISBN:978-0-444-50170-7, pdf]

- Bart Jacobs, p. 122 in:

- Discussion Type
- discussion topicsuper algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 15th 2023

Somebody from the technical team kindly alerted me that we have a full

`.mov`

copy of the video recording of Kapranov 2013 sitting on the nLab server – which is strange (but also lucky), does anyone know/remember how this came to be?In trying to understand what’s going on, I noticed that the relevant YouTube link at Kapranov 2013 had died (“private”) as had my original video link from comment #5 in the original thread. Also the links to the hosting conference had meanwhile rotted away.

I have now

recovered the conference links via the WaybackMachine,

added the link to our local copy of the video recording

and am also uploading the video to YouTube.

Am propagating these edits also to other entries where Kapranov’s talk is referenced, such as at

*Mikhail Kapranov*and at*spectral super-scheme*.

- Discussion Type
- discussion topicsuper 2-algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 15th 2023

I have split of

*super 2-algebra*from super algebra. It’sa stub. Currently the only content is to provide the pointers into the video of Kapranov’s talk (minutes:seconds.)

- Discussion Type
- discussion topicdual bialgebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 15th 2023

Slight extension and new links. However the entry overlaps with more generally scoped entry dual gebra; the overlap will be planned and resolved at a later stage.

- Discussion Type
- discussion topicSegal category
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Aug 15th 2023

polsihed the defnition at Segal category slightly and added a remark on how composition here is an infinity-anafunctor.

- Discussion Type
- discussion topicHarvey Wolff
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Aug 15th 2023

- Discussion Type
- discussion topicvertex operator algebra
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by zskoda
- Last Active Aug 15th 2023

I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here

- Discussion Type
- discussion topicJethro van Ekeren
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 15th 2023

- Discussion Type
- discussion topicmeasurement-based quantum computation
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 15th 2023

- Discussion Type
- discussion topicPoincaré duality space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 14th 2023

added pointer to:

- James Munkres,
*Duality in Manifolds*, Chapter 8 in:*Elements of Algebraic Topology*, Addison-Wesley (1984) [pdf]

- James Munkres,

- Discussion Type
- discussion topichomotopy theory and algebraic topology -- references
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Urs
- Last Active Aug 14th 2023

following discussion here I am starting an entry with a bare list of references (sub-sectioned), to be

`!include`

-ed into the References sections of relevant entries (mainly at*homotopy theory*and at*algebraic topology*) for ease of updating and syncing these lists.The organization of the subsections and their items here needs work, this is just a start. Let’s work on it.

I’ll just check now that I have all items copied, and then I will

`!include`

this entry here into*homotopy theory*and*algebraic topology*. It may best be*viewed*withing these entries, because there – but not here – will there be a table of contents showing the subsections here.

- Discussion Type
- discussion topicPoincaré duality
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Aug 14th 2023

finally an Idea-section at

*Poincaré duality*.(Needs more work, clearly, but should be a start)

- Discussion Type
- discussion topicGavin J. Seal
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicaction monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 13
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicFrobenius monad
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topichomotopy coequalizer
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicobject-oriented programming
- Category Latest Changes
- Started by AlexisHazell
- Comments 57
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topiclens (in computer science)
- Category Latest Changes
- Started by David_Corfield
- Comments 58
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicFrancis J. Murray
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicVenkatesa Chandrasekaran
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 14th 2023

- Discussion Type
- discussion topicvon Neumann algebra factor
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Aug 14th 2023

stub for von Neumann algebra factor

- Discussion Type
- discussion topicCauchy completion
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Aug 13th 2023

“Cauchy completion” and related things were redirecting to both Cauchy complete category and complete space, so I made a disambiguation page.

- Discussion Type
- discussion topicFrank J. Oles
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 13th 2023

- Discussion Type
- discussion topiccategory of descent data
- Category Latest Changes
- Started by DavidRoberts
- Comments 10
- Last comment by zskoda
- Last Active Aug 13th 2023

- Discussion Type
- discussion topicDrinfeld associator
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 13th 2023

Added

- V. G. Drinfeld,
*Quasi-Hopf algebras and Knizhnik-Zanolodchikov equations*, Acad. Sci. Ukrainian SSR, Institute for Theoretical Physics, Preprint ITP-89-43B (Kiev 1989) pdf

P.S. erased later, the reference is not directly appropriate for this entry.

- V. G. Drinfeld,

- Discussion Type
- discussion topicDrinfel'd twist
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Aug 13th 2023

Added the original references

- V. G. Drinfeld,
*Quasi-Hopf algebras and Knizhnik-Zanolodchikov equations*, Acad. Sci. Ukrainian SSR, Institute for Theoretical Physics, Preprint ITP-89-43B (Kiev 1989) pdf - V. G. Drinfel’d,
*Quasi-Hopf algebras*, Algebra i Analiz, 1:6 (1989) 114-148; Leningrad Math. J., 1:6 (1990) 1419-1457 (pdf in Russian) - V. G. Drinfel’d,
*Almost commutative Hopf algebras*, Algebra i Analiz, 1:2 (1989) 30-46; Leningrad Math. J., 1:2 (1990) 321-342 mathnet.ru - Shahn Majid,
*Cross product quantisation, nonabelian cohomology and twisting of Hopf algebras*, in H.-D. Doebner, V.K. Dobrev, A.G. Ushveridze, eds., Generalized symmetries in Physics. World Sci. (1994) 13-41; (arXiv:hep.th/9311184) - Shahn Majid,
*Foundations of quantum group theory*, Cambridge UP

- V. G. Drinfeld,

- Discussion Type
- discussion topiccanonical resolution
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by zskoda
- Last Active Aug 13th 2023

Updated a smidgen to cross-reference with simplicial resolution.

- Discussion Type
- discussion topicquotient module
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Aug 13th 2023

created

*quotient module*

- Discussion Type
- discussion topicSemën S. Kutateladze
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Aug 13th 2023

- Discussion Type
- discussion topicSextus Empiricus
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 13th 2023

- Discussion Type
- discussion topicGottfried Leibniz
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 12th 2023

added pointer to

- Mikhail Katz, David Sherry,
*Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond*(arXiv:1205.0174)

where on the bottom of p. 9 I find

Leibniz rejects nilsquare and nilcube infinitesimals, which are alto-gether incompatible with his approach to differential calculus,

So if not Leibniz, who can be credited with first considering nilpotent infinitesimals?

- Mikhail Katz, David Sherry,

- Discussion Type
- discussion topicWilhemus A. J. Luxemburg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 12th 2023

- Discussion Type
- discussion topicnonstandard analysis
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Aug 12th 2023

I made explicit a subsection on Topos-theoretic models at nonstandard analysis.

Not much there yet, though. I don't really fully understand this yet, but I thought I'd start recording some aspects.

- Discussion Type
- discussion topichomotopy type with finite homotopy groups
- Category Latest Changes
- Started by David_Corfield
- Comments 14
- Last comment by Urs
- Last Active Aug 12th 2023

- Discussion Type
- discussion topicpi-finite type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Aug 12th 2023

- Discussion Type
- discussion topicGigel Militaru
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Aug 12th 2023

- Discussion Type
- discussion topicJiang-Hua Lu
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 12th 2023