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- Discussion Type
- discussion topicquantum channel
- Category Latest Changes
- Started by Eric
- Comments 103
- Last comment by Urs
- Last Active 1 day ago

Wikipedia has a nice article on quantum operations.

The nLab also had a page quantum operations and channels (cache bug?), but I’ve renamed this to simply quantum operation since a quantum channel seems to be nothing but a quantum operation when viewed from the perspective of quantum information theory. Eventually, this page might need some disambiguation since there may be several uses of the term, but for now I think it is “ok”.

I think this page can be cleaned up. I started, but don’t think I will be able to finish.

In particular, there is some background material that might be better on separate pages. I’ll continue trying to clean things up, but family might be calling soon and I’ll need to run quickly whatever state it is in.

I also made the simple statement

In quantum mechanics, a

*quantum operation*is a morphism in the category of density matricesat the beginning of the Idea section motivated by O’Loan’s comment

A quantum channel is a mapping which sends density matrices to density matrices.

This seems innocent enough, but someone might check the statement. For one, I’ve never seen a category of density matrices, but the idea seems obvious enough. Maybe a word on density matrix would be good.

- Discussion Type
- discussion topicdouble field theory
- Category Latest Changes
- Started by Luigi
- Comments 34
- Last comment by Urs
- Last Active 1 day ago

Hello,

I noticed DFT page has not been updated in a while and I added a couple of sections: some sketchy introductory material (analogy between Kaluza-Klein and DFT) and a little insight about a more rigorous geometrical formulation of DFT.

It is still quite sketchy but I would be happy to refine it.

PS: this is my first edit, I hope I played by the rules. And thank you all for this wiki

Luigi

- Discussion Type
- discussion topicCharles Strickland-Constable
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topicC-star-algebra
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by nLab edit announcer
- Last Active 1 day ago

- Discussion Type
- discussion topicpretopological space
- Category Latest Changes
- Started by John Baez
- Comments 1
- Last comment by John Baez
- Last Active 1 day ago

- Discussion Type
- discussion topicCategory Theory conference
- Category Latest Changes
- Started by varkor
- Comments 51
- Last comment by valeriadepaiva
- Last Active 1 day ago

- Discussion Type
- discussion topicMaurer-Cartan form
- Category Latest Changes
- Started by Urs
- Comments 44
- Last comment by Urs
- Last Active 2 days ago

wrote Maurer-Cartan form

the first part is the standard story, but I chose a presentation which I find more insightful than the standard symbol chains as on Wikipedia.

then there is a section on Maurer-Cartan forms on oo-Lie groups and how that reduces to the standard story for ordinary Lie groups.

The detailed statements and proofs of this second part are at Lie infinity-groupoid in the new section The canonical form on a Lie oo-group that is just a Lie group.

- Discussion Type
- discussion topicfactorization algebra
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 2 days ago

added the full definition to factorization algebra

- Discussion Type
- discussion topicheterotic string theory
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active 2 days ago

added pointer to today’s

- Andrea Fontanella, Tomas Ortin,
*On the supersymmetric solutions of the Heterotic Superstring effective action*(arxiv:1910.08496)

- Andrea Fontanella, Tomas Ortin,

- Discussion Type
- discussion topicexceptional tangent bundle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 2 days ago

have added some minimum of references (there were none before)

but I hope to find the time to put some actual content into the entry:

the sequence of exceptional tangent bundles used to be truncated, and the other day I saw (cf. nForum discussion here and here) how to complete it, using recent results.

a pdf note is now here (just 1 page)

- Discussion Type
- discussion topicreflexive coequalizer
- Category Latest Changes
- Started by Mike Shulman
- Comments 16
- Last comment by varkor
- Last Active 3 days ago

Created reflexive coequalizer.

- Discussion Type
- discussion topicfield bundle
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active 3 days ago

- Discussion Type
- discussion topicRamamurti Rajaraman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicsoliton
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicquantum field theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 3 days ago

wrote an Idea-section at quantum field theory

- Discussion Type
- discussion topichyperring
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by RodMcGuire
- Last Active 3 days ago

created hyperring

- Discussion Type
- discussion topicmapping simplex
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 3 days ago

- Discussion Type
- discussion topicSO(32)
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 3 days ago

stub (except for a brief remark on this being the gauge group in type I ST), for the moment just to fill the pattern at

*low dimensional rotation groups – table*

- Discussion Type
- discussion topicEuclidean field theory
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active 4 days ago

am finally adding references here, such as

- Kasper Peeters, Marija Zamaklar,
*Euclidean Field Theory*, Lecture notes 2009-2011 (web, pdf)

will add these also to

*lattice gauge theory*as far as there is overlap- Kasper Peeters, Marija Zamaklar,

- Discussion Type
- discussion topicquaternionic manifold
- Category Latest Changes
- Started by James Francese
- Comments 9
- Last comment by aleks_kleyn
- Last Active 4 days ago

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 112
- Last comment by Ualrus
- Last Active 4 days ago

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 topicprofunctor
- Category Latest Changes
- Started by Mike Shulman
- Comments 32
- Last comment by arbipher
- Last Active 4 days ago

How would people feel about renaming distributor to profunctor? I seem to recall that when this came up on the Cafe, I was the main proponent of the former over the latter, and I've since changed my mind.

- Discussion Type
- discussion topicontology log
- Category Latest Changes
- Started by Corbin
- Comments 3
- Last comment by Corbin
- Last Active 4 days ago

- Discussion Type
- discussion topicE₉
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Added redirect for “E9” at the bottom of the page.)

- Discussion Type
- discussion topicRalf Köhl
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicRobin Lautenbacher
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicKac-Moody algebra
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 4 days ago

I have half-heartedly started adding something to

*Kac-Moody algebra*. Mostly refrences so far. But I don’t have the time right now to do any more.

- Discussion Type
- discussion topicE₁₁
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active 4 days ago

have added a minimum on the level decompositon of the first fundamental rep of $E_{11}$ here.

- Discussion Type
- discussion topichistory of inductive types – references
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by varkor
- Last Active 5 days ago

a bare list of references, to be

`!include`

-ed into the References-lists of relevant entries (*inductive type*,*inductive familiy*,*inductive-recursive family*,*calculus of inductive constructions*)this list includes a polished-up version of

all the references previously listed at

*inductive familiy*in the section “History” (due to revisions $\leq 5$ by Bas Spitters)further references previously listed at

*inductive-recursive type*

and some more

- Discussion Type
- discussion topictraced monoidal category
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active 5 days ago

created

*traced monoidal category*with a bare minimumI would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.

- Discussion Type
- discussion topicVopěnka's principle
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active 5 days ago

Added:

The large cardinal strength of the weak Vopěnka principle is discussed in

- Trevor M. Wilson,
*The large cardinal strength of Weak Vopěnka’s Principle*, arXiv.

The following paper shows that weak Vopěnka’s principle is indeed weaker than Vopěnka’s principle:

- Trevor M. Wilson,
*Weak Vopěnka’s Principle does not imply Vopěnka’s Principle*, arXiv.

- Trevor M. Wilson,

- Discussion Type
- discussion topicYang-Mills equation
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active 5 days ago

- Discussion Type
- discussion topicBi-Yang-Mills equation
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active 5 days ago

Created new article for Bi-Yang-Mills equation. (The english and german Wikipedia article are now also available.)

- Discussion Type
- discussion topicF-Yang-Mills equation
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active 5 days ago

Created new article for F-Yang-Mills equation. (The english and german Wikipedia article are now also available.)

- Discussion Type
- discussion topicfunctor comprehension principle
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by maxsnew
- Last Active 5 days ago

copied article from the michaelshulman wiki at functor comprehension principle (michaelshulman) to the nlab wiki.

C. Silva

- Discussion Type
- discussion topicG-spectrum
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active 5 days ago

I am touching various entries related to equivariant stable homotopy theory, adding basics from the literature. For instance I briefly added to

*G-spectrum*the basic definition via indexing on a universe, and added the statement of the equivariant stable Whitehead theorem, cross-linked with the relevant bits at*equivariant homotopy theory*, etc. I have also been expanding a little more at*RO(G)-grading*and cross-linked more with old material at*equivariant cohomology*. Tried to make the link between RO(G)-grading and equivariant suspension isomorphism more explicit.Just in case you are watching the logs and are wondering. I am not announcing every single edit, unless there is anything noteworthy.

- Discussion Type
- discussion topiccrystal (algebraic geometry)
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active 6 days ago

- Discussion Type
- discussion topicEdison M. Murairi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicexceptional field theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 6 days ago

started some minimum at

*exceptional field theory*(the formulation of 11d supergravity that makes the exceptional U-duality symmetry manifest)

- Discussion Type
- discussion topicDaniel Butter
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicMarc Krasner
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicRiemann zeta function
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Tom Mainiero
- Last Active 7 days ago

have added a tad more to the Properties-section at

*Riemann zeta function*.

- Discussion Type
- discussion topicnotions of subcategory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active 7 days ago

have created a “floating TOC”

*notions of subcategory*and have included it in the relevant entries

- Discussion Type
- discussion topicAlexander G. Tumanov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 2nd 2024

- Discussion Type
- discussion topicThomas Fischbacher
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 2nd 2024

- Discussion Type
- discussion topicLuca Carlevaro
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 2nd 2024

- Discussion Type
- discussion topicE₁₀
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 4
- Last comment by Urs
- Last Active Nov 2nd 2024

Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “E10” from the top and added one for “E10” at the bottom of the page.)

- Discussion Type
- discussion topicM-theory
- Category Latest Changes
- Started by David_Corfield
- Comments 27
- Last comment by Urs
- Last Active Nov 2nd 2024

A stub for M-theory. What’s supposed to be so mysterious about it? Is it that people don’t even know what form it would take?

- Discussion Type
- discussion topicThe Unreasonable Effectiveness of Mathematics in the Natural Sciences
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 2nd 2024

- Discussion Type
- discussion topicCharles Wells
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active Nov 2nd 2024

the link to the picture in the entry

*Charles Wells*is broken. Does anyone know how to fix it or have an alternative picture?

- Discussion Type
- discussion topicslice theorem
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by nLab edit announcer
- Last Active Nov 1st 2024

- Discussion Type
- discussion topicrigid topology
- Category Latest Changes
- Started by Thomas Holder
- Comments 1
- Last comment by Thomas Holder
- Last Active Nov 1st 2024

- Discussion Type
- discussion topicToposes of laws of motion
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 1st 2024

- Discussion Type
- discussion topiccomputable physics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 1st 2024

- Discussion Type
- discussion topicautomaton
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 1st 2024

Added this pointer:

An early discussion of automata via string diagrams in the Cartesian monoidal category of finite sets:

- Günter Hotz,
*Eine Algebraisierung des Syntheseproblems von Schaltkreisen*, EIK, Bd. 1, (185-205), Bd, 2, (209-231) 1965 (part I, part II, compressed and merged pdf)

incuding that new compressed and merged pdf which I produced, as a service to the community.

- Günter Hotz,

- Discussion Type
- discussion topiccomputation
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Nov 1st 2024

In looking for texts that would address the question “What is computation?” and arrive at an answer vaguely akin to path lifting/transport, I found (and have now added pointer to) this text:

- Jan van Leeuwen, Jiří Wiedermann:
*Knowledge, Representation and the Dynamics of Computation*, pp. 69-89 in:*Representation and Reality in Humans, Other Living Organisms and Intelligent Machines*, Studies in Applied Philosophy, Epistemology and Rational Ethics**28**, Springer (2017) [doi:10.1007/978-3-319-43784-2_5, pdf]

which gets pretty close, in particular in and around their Figure 1.

- Jan van Leeuwen, Jiří Wiedermann:

- Discussion Type
- discussion topicconstructive mathematics
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Nov 1st 2024

I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to

- Discussion Type
- discussion topiclocally cartesian closed category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by Urs
- Last Active Oct 31st 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 topiclinearly distributive category
- Category Latest Changes
- Started by Mike Shulman
- Comments 37
- Last comment by nLab edit announcer
- Last Active Oct 31st 2024

I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how $*$-autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.

- Discussion Type
- discussion topicvirtual double category
- Category Latest Changes
- Started by maxsnew
- Comments 16
- Last comment by varkor
- Last Active Oct 31st 2024

I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.