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- Discussion Type
- discussion topictensor product of chain complexes
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by nLab edit announcer
- Last Active Sep 7th 2023

following public demand, I added to

*tensor product of chain complexes*a detailed elementary discussion of the tensor product $I_\bullet \otimes I_\bullet$ of the (normalized) chain interval with itself, and how it gives chains on the cellular square: in*Square as tensor product of interval with itself*.

- Discussion Type
- discussion topicCarlo Angiuli
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicsynthetic Tait computability
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by jonsterling
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicAllan L. Edelson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicWedderburn-Artin theorem
- Category Latest Changes
- Started by John Baez
- Comments 5
- Last comment by John Baez
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicreal vector bundle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicmodule object
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 6th 2023

expanded the Idea-section and added a reference:

- Francis Borceux, George Janelidze, Gregory Maxwell Kelly, p. 8 of:
*Internal object actions*, Commentationes Mathematicae Universitatis Carolinae (2005) Volume: 46, Issue: 2, page 235-255 (dml:249553)

- Francis Borceux, George Janelidze, Gregory Maxwell Kelly, p. 8 of:

- Discussion Type
- discussion topicFlorian Marty
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topicAbhishek Banerjee
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 6th 2023

- Discussion Type
- discussion topiccommutative monoid in a symmetric monoidal category
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 6th 2023

added the examples of differential graded-commutative algebras and of differential graded-commutative superalgebras

- Discussion Type
- discussion topicCategory Theory conference
- Category Latest Changes
- Started by varkor
- Comments 49
- Last comment by varkor
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicOberwolfach
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by varkor
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicHermitian form
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topiccomplex structure
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 5th 2023

stub for complex structure

- Discussion Type
- discussion topiclinear algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicAlexey O. Remizov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 5th 2023

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

wrote a sentence at

*complexification*

- Discussion Type
- discussion topicKaya Arro
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicrepresentation stability
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicdistributivity of limits over colimits
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 13
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topichomotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 63
- Last comment by Urs
- Last Active Sep 5th 2023

stub for homotopy type theory

- Discussion Type
- discussion topicmodal type theory
- Category Latest Changes
- Started by Urs
- Comments 99
- Last comment by Urs
- Last Active Sep 5th 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 topicAlan Robinson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 5th 2023

- Discussion Type
- discussion topic!-modality
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by David_Corfield
- Last Active Sep 5th 2023

collected some references on the interpretation of the !-modality as the Fock space construction at

*!-modality*.Cross-linked briefly with he stub entries_Fock space_ and

*second quantization*.

- Discussion Type
- discussion topicnonunital ring
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Todd_Trimble
- Last Active Sep 5th 2023

Added:

A survey of various notions between unital rings and nonunital rings:

- Patrik Nystedt,
*A survey of s-unital and locally unital rings*, Revista Integración, temas de matemáticas Escuela de Matemáticas, Universidad Industrial de Santander, Vol. 37, N◦ 2, 2019, pág. 251–260. doi.

- Patrik Nystedt,

- Discussion Type
- discussion topiccharacteristic polynomial
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicWagner-Preston theorem
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Sep 5th 2023

- Discussion Type
- discussion topicheap
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 16
- Last comment by zskoda
- Last Active Sep 4th 2023

- Discussion Type
- discussion topicregular category
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 4th 2023

added publication details for this reference:

- F. Cagliari, S. Mantovani, Enrico Vitale,
*Regularity of the category of Kelley spaces*, Applied Categorical Structures volume 3, pages 357–361 (1995) (doi:10.1007/BF00872904, pdf)

and am copying it over to

*compactly generated topological space*, too- F. Cagliari, S. Mantovani, Enrico Vitale,

- Discussion Type
- discussion topicCayley's theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Sep 4th 2023

creating a minimum entry, to satisfy long-requested links in entries such as

*permutation group**heap*

- Discussion Type
- discussion topiclinear logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 41
- Last comment by Urs
- Last Active Sep 4th 2023

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

- Discussion Type
- discussion topicAlexei P. Kopylov
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2023

- Discussion Type
- discussion topicaffine logic
- Category Latest Changes
- Started by David_Corfield
- Comments 15
- Last comment by Urs
- Last Active Sep 4th 2023

I started a stub at affine logic as I saw the link requested in a couple of places.

- Discussion Type
- discussion topicfuzzy sphere
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Sep 4th 2023

- Discussion Type
- discussion topicMaximilian Rupprecht
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2023

- Discussion Type
- discussion topicKlaus Dietz
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2023

- Discussion Type
- discussion topicNicolai map
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2023

mostly to collect some references, prodded by today’s review:

- Olaf Lechtenfeld,
*The Nicolai-map approach to supersymmetry*[arXiv:2309.00481]

- Olaf Lechtenfeld,

- Discussion Type
- discussion topicBorn rule
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 3rd 2023

a bare minimum, for the moment just to make links work (such as at

*probability amplitude*and at*Wigner’s theorem*)

- Discussion Type
- discussion topicmonadic functor
- Category Latest Changes
- Started by Alec Rhea
- Comments 13
- Last comment by Urs
- Last Active Sep 2nd 2023

The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.

- Discussion Type
- discussion topicmonoidal functor
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Sep 2nd 2023

created (finally) lax monoidal functor (redirecting monoidal functor to that) and strong monoidal functor.

Hope I got the relation to 2-functors right. I remember there was some subtlety to be aware of, but I forget which one. I could look it up, but I guess you can easily tell me.

- Discussion Type
- discussion topicmonoidal natural transformation
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Urs
- Last Active Sep 2nd 2023

We had a stub at symmetric monoidal natural transformation but not at monoidal natural transformation, so I put one there.

- Discussion Type
- discussion topicPeter Schauenburg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 1st 2023

- Discussion Type
- discussion topicstrict monoidal category
- Category Latest Changes
- Started by J-B Vienney
- Comments 3
- Last comment by Urs
- Last Active Sep 1st 2023

- Discussion Type
- discussion topicdependent linear type theory
- Category Latest Changes
- Started by Urs
- Comments 88
- Last comment by Urs
- Last Active Sep 1st 2023

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 topicfunny tensor product
- Category Latest Changes
- Started by Mike Shulman
- Comments 15
- Last comment by varkor
- Last Active Sep 1st 2023

Finally created funny tensor product. This is not really a very good name for a serious mathematical concept, but I don’t know of a better one.

- Discussion Type
- discussion topicsesquicategory
- Category Latest Changes
- Started by FinnLawler
- Comments 23
- Last comment by varkor
- Last Active Sep 1st 2023

New page at sesquicategory.

- Discussion Type
- discussion topicmonoidal monad
- Category Latest Changes
- Started by Todd_Trimble
- Comments 17
- Last comment by Urs
- Last Active Sep 1st 2023

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 topicHopf algebra
- Category Latest Changes
- Started by Urs
- Comments 35
- Last comment by perezl.alonso
- Last Active Sep 1st 2023

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

- Discussion Type
- discussion topicPaul Dirac
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 1st 2023

added these references, and added their doi etc.:

Early speculations trying to model the electron by a relativistic membrane:

{#Dirac62} Paul Dirac,

*An Extensible Model of the Electron*, Proc. Roy. Soc. A268, (1962) 57-67 (jstor:2414316)Paul Dirac,

*The motion of an Extended Particle in the Gravitational Field*, in Relativistic Theories of Gravitation, Proceedings of a Conference held in Warsaw and Jablonna, July 1962, ed. L. Infeld, P. W. N. Publishers, 1964, Warsaw, 163-171; discussion 171-175 (spire:1623740)Paul Dirac,

*Particles of Finite Size in the Gravitational Field*, Proc. Roy. Soc. A270, (1962) 354-356 (doi:10.1098/rspa.1962.0228)

- Discussion Type
- discussion topicfinite-dimensional Hilbert space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 1st 2023

- Discussion Type
- discussion topictangent (infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 56
- Last comment by David_Corfield
- Last Active Sep 1st 2023

I rewrote the few sentences at tangent (infinity,1)-category in an attempt to make it run more smoothly.

In any case, there is not much there yet...

- Discussion Type
- discussion topicquantum measurement
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Aug 31st 2023

created a currently fairly empty entry

*quantum measurement*, just so as to have a place where to give a commented pointer to the article- Klaas Landsman, Robin Reuvers,
*A Flea on Schrödinger’s Cat*, Found. Phys. 43, 373-407 (2013) (arXiv:1210.2353)

- Klaas Landsman, Robin Reuvers,

- Discussion Type
- discussion topicwell-order
- Category Latest Changes
- Started by Todd_Trimble
- Comments 14
- Last comment by TobyBartels
- Last Active Aug 31st 2023

I made some edits at well-order. I am removing a query box, having duly extracted some punchlines. These edits also forced an edit to partial function, where I added the generalization to partial maps in any category with pullbacks.

+– {: .query} This need not exist; in particular, $S_a$ may be empty. What do we really want to say here? (We could talk about the successor

*of*a well-ordered set.) —Toby Mike: Yeah, or we could say that successor is a partial function. One definition of a limit ordinal is one on which successor is totally defined. =–

- Discussion Type
- discussion topicbialgebra cocycle
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by perezl.alonso
- Last Active Aug 31st 2023

- Discussion Type
- discussion topicHartogs number
- Category Latest Changes
- Started by Todd_Trimble
- Comments 34
- Last comment by Todd_Trimble
- Last Active Aug 31st 2023

Added a bit to Hartogs number. Including the curiosity that GCH implies AC. :-)

- Discussion Type
- discussion topicstar-algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 31st 2023

I have made explicit the example of involutive Hopf algebras, and how most of the other examples previously listed here are special cases of this one. Also expanded a little and organized it all into a new Examples-subsection (here)

- Discussion Type
- discussion topicAT category
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by David_Corfield
- Last Active Aug 31st 2023

slightly edited

*AT category*to make the definition/lemma/proposition-numbering and cross-referencing to them come out.Probably Todd should have a look over it to see if he agrees.

- Discussion Type
- discussion topicLuigi Bianchi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 31st 2023

- Discussion Type
- discussion topicbilinear form
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 31st 2023

it has annoyed me for a long time that bilinear form did not exist. Now it does. But not much there yet.

- Discussion Type
- discussion topicinhomogeneous cosmology
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by Urs
- Last Active Aug 31st 2023

started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective