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- Discussion Type
- discussion topicbit flip code
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 25th 2022

- Discussion Type
- discussion topicconcept with an attitude
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Nov 25th 2022

This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:

In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.

Here are examples:

A

*quiver*is just a directed graph (pseudograph, to be explicit). But one says*quiver*instead of*directed graph*when one is interested in studying*quiver representations*: functors from the free category on that graph to the category of finite-dimensional vector spaces.A

*presheaf*is just a contravariant functor. But one says*presheaf*instead of*contravariant functor*when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.

(…)

- Discussion Type
- discussion topicabstract rewriting system
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by Urs
- Last Active Nov 25th 2022

- Discussion Type
- discussion topiccomonoid
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by Urs
- Last Active Nov 25th 2022

- Discussion Type
- discussion topicordinal number
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 24th 2022

removing old comment in query box

+– {: .query}

*Madeleine Birchfield*: Wouldn’t an ordinal number be an object of the decategorification of the category of well-ordered sets, just as a natural number is an object of the decategorification of the category FinSet? =–Anonymous

- Discussion Type
- discussion topicbiproduct
- Category Latest Changes
- Started by Colin Tan
- Comments 19
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

- Discussion Type
- discussion topicCMon-enriched monoidal category
- Category Latest Changes
- Started by J-B Vienney
- Comments 8
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 100
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

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 topicrewriting
- Category Latest Changes
- Started by David_Corfield
- Comments 9
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

I thought to add

- Amar Hadzihasanovic,
*Diagrammatic sets and rewriting in weak higher categories*, (arXiv:2007.14505)

- Amar Hadzihasanovic,

- Discussion Type
- discussion topiccategory of monoids
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

started entry on category of monoids. Spelled out the free monoid construction. Stated the construction of pushouts of monoids along free maps with reference to Schwede-Shipley. Will fill in the proof in a moment.

- Discussion Type
- discussion topicRing
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

- Discussion Type
- discussion topicprimitive element
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

I have added to

*primitive element*the definition of primitive elements in comodules, and their equivalent characterization in terms of cotensor products. Added also a corresponding remark to cotensor product.

- Discussion Type
- discussion topicmodule
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by J-B Vienney
- Last Active Nov 24th 2022

I started to greatly expand the entry module

The new toc now looks like this:

Idea

Basic idea

More general perspectives

Enriched presheaves

Stabilized overcategories

Details

Ordinary concept

In enriched category theory

Examples

- Modules over rings

Related concepts

- Vector bundles and sheaves of modules

- Discussion Type
- discussion topicdegree of a polynomial
- Category Latest Changes
- Started by nLab edit announcer
- Comments 15
- Last comment by nLab edit announcer
- Last Active Nov 24th 2022

- Discussion Type
- discussion topicflavour anomaly
- Category Latest Changes
- Started by Urs
- Comments 193
- Last comment by Urs
- Last Active Nov 24th 2022

- Discussion Type
- discussion topichomogeneous polynomial
- Category Latest Changes
- Started by J-B Vienney
- Comments 3
- Last comment by nLab edit announcer
- Last Active Nov 24th 2022

- Discussion Type
- discussion topicsynthetic guarded domain theory
- Category Latest Changes
- Started by maxsnew
- Comments 23
- Last comment by maxsnew
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicRibet's theorem
- Category Latest Changes
- Started by Anton Hilado
- Comments 1
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicShimura variety
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicLanglands program
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

added pointer to

- Joseph Bernstein, Stephen Gelbart (eds.),
*An Introduction to the Langlands Program*, Springer 2018 (doi:10.1007/978-0-8176-8226-2)

- Joseph Bernstein, Stephen Gelbart (eds.),

- Discussion Type
- discussion topicLanglands functoriality
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

Added a reference to Langlands functoriality:

- Minhyong Kim,
*A superficial introduction to Langlands functoriality*, slides

Are we any closer to

From this perspective Langlands’s “functoriality” is Lurie’s “global equivariance”…

- Minhyong Kim,

- Discussion Type
- discussion topicHeine-Borel theorem
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Nov 23rd 2022

stub for

*Heine-Borel theorem*

- Discussion Type
- discussion topicquantum circuits via dependent linear types
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Nov 23rd 2022

Am starting a write-up (here) of how (programming languages for) quantum circuits “with classical control and/by measurement” have a rather natural and elegant formulation within the linear homotopy type theory of Riley 2022.

Aspects of this have a resemblance to some constructions considered in/with “Quipper”, but maybe it helps clarify some issues there, such as that of “dynamic lifting”.

The entry is currently written without TOC and without Idea-section etc, but rather as a single top-level section that could be

`!include`

-ed into relevant entries (such as at*quantum circuit*and at*dependent linear type theory*). But for the moment I haven’t included it anywhere yet, and maybe I’ll eventually change my mind about it.

- Discussion Type
- discussion topicgraded algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by J-B Vienney
- Last Active Nov 23rd 2022

added pointer to:

- Gregory Karpilovsky, Chapter 2 of:
*The Algebraic Structure of Crossed Products*, Mathematics Studies**142**, North Holland 1987 (ISBN:9780080872537)

- Gregory Karpilovsky, Chapter 2 of:

- Discussion Type
- discussion topicmodular form
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

added to

*modular form*a brief paragraph with a minimum of information on modular forms*As automorphic forms*. Needs to be expanded.

- Discussion Type
- discussion topicsymmetric algebra
- Category Latest Changes
- Started by J-B Vienney
- Comments 4
- Last comment by J-B Vienney
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicbimonoid
- Category Latest Changes
- Started by Mike Shulman
- Comments 12
- Last comment by J-B Vienney
- Last Active Nov 23rd 2022

Added to bimonoid the fact that the category of modules over a bimonoid is monoidal.

- Discussion Type
- discussion topicanalytic ring
- Category Latest Changes
- Started by Anton Hilado
- Comments 10
- Last comment by Guest
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicSiegel upper half-space
- Category Latest Changes
- Started by Anton Hilado
- Comments 3
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicSiegel modular form
- Category Latest Changes
- Started by Anton Hilado
- Comments 2
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicPeter Scholze
- Category Latest Changes
- Started by Anton Hilado
- Comments 1
- Last comment by Anton Hilado
- Last Active Nov 23rd 2022

- Discussion Type
- discussion topicdialgebra
- Category Latest Changes
- Started by varkor
- Comments 11
- Last comment by David_Corfield
- Last Active Nov 22nd 2022

The page on inductive-inductive types refers to dialgebras without specifying them. Having a short page as some sort of reference is helpful.

- Discussion Type
- discussion topiclocal field (commutative algebra)
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topiccommutative monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 7
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicmonoidal monad
- Category Latest Changes
- Started by Todd_Trimble
- Comments 14
- Last comment by Urs
- Last Active Nov 22nd 2022

Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).

- Discussion Type
- discussion topicstrong monad
- Category Latest Changes
- Started by Sam Staton
- Comments 27
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicAndrew Kent
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topiclinear type theory
- Category Latest Changes
- Started by Urs
- Comments 45
- Last comment by Urs
- Last Active Nov 22nd 2022

Am trying to get some historical citations straight at

*linear type theory*, maybe somebody can help me:what are the original sources of the idea that linear logic/type theory should generally be that of symmetric monoidal categories (“multiplicative intuitionistic LL”)?

In order of appearance, I am aware of

de Paiva 89 gives one particular example of a non-star-autonomous SMC that deserves to be said to interpret “linear logic” and clearly identifies the general perspective.

Bierman 95 discusses semantics in general SMCs more generally

Barber 97 reviews this and explores a bit more.

What (other) articles would be central to cite for this idea/perspective?

I am aware of more recent reviews such as

but I am looking for the correct “original sources”.

- Discussion Type
- discussion topicclass theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicp-adic Teichmüller theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicKirti Joshi
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 22nd 2022

brief

`category:people`

-entry for satisfying links now requested at*p-adic Teichmüller theory*

- Discussion Type
- discussion topicpartial function
- Category Latest Changes
- Started by Urs
- Comments 31
- Last comment by nLab edit announcer
- Last Active Nov 22nd 2022

added to

*partial function*a new section*Definition – General abstract*with a brief paragraph on how partial functions form the Kleisli category of the maybe-monad.

- Discussion Type
- discussion topicMartin Greiter
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicD=4 supergravity
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 22nd 2022

- Discussion Type
- discussion topicFAC
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 22nd 2022

New reference entry FAC aka Faisceaux algébriques cohérents. And few improvements to coherent sheaf including historical note.

- Discussion Type
- discussion topicVectBund
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

starting a dedicated entry for the category of vector bundles with homomorphisms allowed to cover non-trivial base maps (while previously we only had VectBund(B) for fixed base $B$).

For the moment the main point is to record the interesting cartesian- and tensor-monoidal structure (now here)

- Discussion Type
- discussion topicblack hole information paradox
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 21st 2022

added pointer also to this recent review in a popular magazine, which is well-informed about the contested status of the “island conjecture”:

Nirmalya Kajuri,

*Of Islands, Holograms and Saving Quantum Physics From a Black Hole Paradox*, Science – The Wire (Nov 2022)[…] a few sceptics have argued that while the calculations are correct, they don’t help resolve the black hole information-loss paradox. The troubles stem from the reservoir attached to the anti-de Sitter universe. The physicists who authored the island papers assumed that gravity stopped at the boundary of the anti-de Sitter space and didn’t enter the reservoir. This is not an innocuous assumption. […] The key takeaway is that the island way to recover information and save unitarity works perfectly well – if you slightly modify Einstein’s theory of gravity. These criticisms have been around for some two years now, and physicists are yet to resolve them in print. […] physicists continue to publish papers by the hundreds about the entanglement islands but few attempt to answer whether the islands are compatible with the Einsteinian gravity of our universe. […]

I think i will create an

`include`

-file now for these references, so that it will be easier to sync with other entrties, such as*Bekenstein-Hawking entropy*:

- Discussion Type
- discussion topicVect(X)
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 21st 2022

Created a little entry

*Vect(X)*(to go along with*Vect*) and used the occasion to give*distributive monoidal category*the Examples-section that it was missing and similarly touched the Examples-section at*rig category*.

- Discussion Type
- discussion topicKirill Shtengel
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicJoost Slingerland
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicMikhail Khovanov
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Urs
- Last Active Nov 21st 2022

Added an article

- Mikhail Khovanov, Robert Lipshitz,
*Categorical lifting of the Jones polynomial: a survey*, Bulletin (New Series) of the American Mathematical Society (doi:10.1090/bull/1772)

- Mikhail Khovanov, Robert Lipshitz,

- Discussion Type
- discussion topicsubring
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicMatthew Morrow
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicMatthew Emerton
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicLucas Mann
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2022

- Discussion Type
- discussion topicopen problem of confinement -- references
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Nov 21st 2022

a bare sub-section with a list of references – to be

`!included`

into relevant entries – mainly at*confinement*and at*mass gap problem*(where this list already used to live)

- Discussion Type
- discussion topicquantum gravity
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Nov 21st 2022

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

- Discussion Type
- discussion topicétale homotopy
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by nLab edit announcer
- Last Active Nov 20th 2022

I made

*étale homotopy*and*étale homotopy theory*be redirects to the entry geometric homotopy groups in an (infinity,1)-topos

- Discussion Type
- discussion topicNirmalya Kajuri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 20th 2022

- Discussion Type
- discussion topicsplit property
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 20th 2022