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- Discussion Type
- discussion topicposet of subobjects
- Category Latest Changes
- Started by Peter Heinig
- Comments 17
- Last comment by Hurkyl
- Last Active May 4th 2020

poset of subobjects did not yet have a remark on the frequently occurring question whether to define subobjects as morphisms or as isomorphism

*classes*thereof, nor did it yet (seem) to have a thread. Added both. In particular, added the phrase “groupoid of subobjects”. Added two reference where the morphism-versus-class-of-morphisms issue is discussed. Refrained from making any recommendations or comparisions, only writing “alternative definition”.Whenever I see this topic coming up, I am reminded of the “Isomorphic types are equal?!” debate.

Since I do not have much experience in this debate, I shy away from trying to connect isomorphic-types-are-equal with poset of subobjects, but it seems to me that something relevant could be said in this regard in poset of subobjects by someone more experienced.

- Discussion Type
- discussion topicCharles Hermite
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

brief

`category:people`

-entry for hyperlinking references at*Hermite polynomial*,*countable set*and*pi*(if we mention him at*pi*, somebody should reall mention him at*Euler number*)

- Discussion Type
- discussion topichypergeometric function
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

- Discussion Type
- discussion topicrelation between 5d Maxwell theory and self-dual 3-forms in 6d -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

This is a bare sub-section, to be

`!include`

-ed into relevant entries (at*D=5 Maxwell theory*, at*self-dual higher gauge theory*and at*Perry-Schwarz Lagrangian*).

- Discussion Type
- discussion topicD=5 Einstein-Maxwell theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

a stub, for the moment just so as to complete a pattern of entries, but I added pointer to

Paul Wesson,

*Space-Time-Matter: Modern Kaluza-Klein Theory*, World Scientific 1989 (doi:10.1142/3889)Paul Wesson, James M. Overduin,

*Principles of Space-Time-Matter: Cosmology, Particles and Waves in Five Dimensions*, World Scientific 2018 (doi:10.1142/10871)

- Discussion Type
- discussion topicPaul Wesson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

brief

`category:people`

-entry for hyperlinking references at*Kaluza-Klein theory*and*5d electromagnetism*

- Discussion Type
- discussion topicKaluza-Klein mechanism
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active May 4th 2020

recently there were some questions about it here on the nForum: now there is an entry on the Kaluza-Klein mechanism

- Discussion Type
- discussion topicBF-theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 4th 2020

Added to BF-theory the reference that right now I am believing is the earliest one:

Gary Horowitz,

*Exactly soluable diffeomorphism invariant theories*Commun. Math. Phys. 125, 417-437 (1989)But maybe I am wrong. Does anyone have an earlier one? I saw pointers to A. Schwarz articles from the late 70s, but I am not sure if he really considered BF as such.

- Discussion Type
- discussion topicMagnus Carlson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 4th 2020

bief

`category:people`

-entry, for hyperlinking the reference- Magnus Carlson, Minhyong Kim,
*A note on abelian arithmetic BF-theory*, (arXiv:1911.02236)

that has been asking for this link since January 2020 (here)

- Magnus Carlson, Minhyong Kim,

- Discussion Type
- discussion topiclocally finitely presentable category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by David_Corfield
- Last Active May 4th 2020

I’m making some edits to locally finitely presentable category, and removing some old query boxes. A punchline was extracted, I believe, from the first query box. The second I don’t think is too important (it looks like John misunderstood).

+–{: .query} Mike: Do people really call finitely presentable

*objects*“finitary”? I’ve only seen that word applied to functors (those that preserve filtered colimits). Toby: I have heard ’finite’; see compact object.*Mike*: Yes, I’ve heard ’finite’ too. =–+– {: .query} Toby: In the list of equivalent conditions above, does this essentially algebraic theory also have to be finitary?; that is, if it's an algebraic theory, then it's a Lawvere theory?

Mike: Yes, it certainly has to be finitary. Possibly the standard meaning of “essentially algebraic” implies finitarity, though, I don’t know.*Toby*: I wouldn't use ’algebraic’ that way; see algebraic theory. John Baez: How come the first sentence of this paper seems to suggest that the category of models of*any*essentially algebraic theory is locally finitely presentable? The characterization below, which I did not write, seems to agree. Here there is no restriction that the theory be finitary. Does this contradict what Mike is saying, or am I just confused?

*Mike*: The syntactic category of a non-finitary essentially algebraic theory is not a category with finite limits but a category with $\kappa$-limits where $\kappa$ is the arity of the theory. A finitary theory can have infinitely many sorts and operations; what makes it finitary is that each operation only takes finitely many inputs, hence can be characterized by an arrow whose domain is a finite limit. I think this makes the first sentence of that paper completely consistent with what I’m saying. =–

- Discussion Type
- discussion topiclight-cone gauge quantization
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 4th 2020

created a bare minimum at

*light-cone gauge quantization*, just so as to be able to sensibly link to it from elsewhere

- Discussion Type
- discussion topicclass-locally presentable category
- Category Latest Changes
- Started by DavidRoberts
- Comments 3
- Last comment by DavidRoberts
- Last Active May 4th 2020

- Discussion Type
- discussion topicHodge star operator on Minkowski spacetime -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2020

This is a page with fully explicit component computations of properties of the Hodge star operator on Minkowski spacetime. It is a bare sub-section, to be

`!include`

-ed inside sections of relevant entries (under “Examples” at*Hodge star operator*and under “Properties” at*Minkowski spacetime*)

- Discussion Type
- discussion topiccrystallographic group
- Category Latest Changes
- Started by David_Corfield
- Comments 21
- Last comment by Todd_Trimble
- Last Active May 3rd 2020

- Discussion Type
- discussion topicHegelian taco
- Category Latest Changes
- Started by DavidRoberts
- Comments 11
- Last comment by Thomas Holder
- Last Active May 3rd 2020

Thomas Holder is busy creating Hegelian taco as I write.

- Discussion Type
- discussion topicDaniel Schroeder
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2020

brief

`category:people`

-entry for hyperlinking references at*perturbative quantum field theory*

- Discussion Type
- discussion topicfield-strength renormalization
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2020

- Discussion Type
- discussion topicover category
- Category Latest Changes
- Started by Bubbles
- Comments 50
- Last comment by Urs
- Last Active May 3rd 2020

- In codomain fibration one calls the function

C \ (-) : C --> Cat

mapping c to the slice category (C \ c) a pseudofunctor. However I fail to see how this is not functorial.

A morphism f : a --> b is sent to the functor (C \ f) : (C \ a) --> (C \ b) defined by (g : c --> a) |--> (fg : c --> b), and this assignment clearly satisfies composition. It also preserves identity. So what am I missing here?

- Discussion Type
- discussion topicunder category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2020

copied over, from

*overcategory*, statement and proof of computing limits in undercategories

- Discussion Type
- discussion topicDieter Schildknecht
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active May 3rd 2020

brief

`category:people`

-entry for hyperlinking references at*vector meson dominance*

- Discussion Type
- discussion topicvector meson dominance
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active May 3rd 2020

- Discussion Type
- discussion topicgraphic category
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Richard Williamson
- Last Active May 3rd 2020

John Baez added to graphic category some facts noticed at the cafe; I made left shelf a link and added the appropriate redirect to rack.

- Discussion Type
- discussion topicelectroweak symmetry breaking
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 3rd 2020

added pointer to

- Gautam Bhattacharyya,
*A Pedagogical Review of Electroweak Symmetry Breaking Scenarios*, Rept. Prog. Phys. 74:026201, 2011 (arXiv:0910.5095)

and publication data to

- Antonio Pich,
*Electroweak Symmetry Breaking and the Higgs Boson*, Acta Phys. Pol. B 47, 151 (2016) (arXiv:1512.08749)

- Gautam Bhattacharyya,

- Discussion Type
- discussion topicGeorge Janelidze
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active May 3rd 2020

- Discussion Type
- discussion topicaxiom of choice
- Category Latest Changes
- Started by Mike Shulman
- Comments 8
- Last comment by Todd_Trimble
- Last Active May 2nd 2020

I’m not entirely happy with the introduction (“Statement”) to the page axiom of choice. On the one hand, it implies that the axiom of choice is something to be considered relative to a given category $C$ (which is reasonable), but it then proceeds to give the

*external*formulation of AC for such a $C$, which I think is usually not the best meaning of “AC relative to $C$”. I would prefer to give the Statement as “every surjection in the category of sets splits” and then discuss later that analogous statements for other categories (including both internal and external ones) can also be called “axioms of choice” — but with emphasis on the internal ones, since they are what correspond to the original axiom of choice (for sets) in the internal logic.(I would also prefer to change “epimorphism” for “surjection” or “regular/effective epimorphism”, especially when generalizing away from sets.)

- Discussion Type
- discussion topicintegral domain
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active May 2nd 2020

- Discussion Type
- discussion topicparametric right adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by Todd_Trimble
- Last Active May 2nd 2020

Added alternative terminology “local right adjoint” and “strongly cartesian monad” from Berger-Mellies-Weber. They claim the former “has become the more accepted terminology” than “parametric right adjoint”; does anyone know other references to support this? (I think it’s certainly more logical, in that it fits with the general principle of “local” meaning “on slice categories” — not to be confused with the different general principle of “local” meaning “in hom-objects”.)

- Discussion Type
- discussion topiccategory of presheaves
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Todd_Trimble
- Last Active May 2nd 2020

I felt there should be an entry category of presheaves. So I started one.

- Discussion Type
- discussion topicordinal sum
- Category Latest Changes
- Started by Tim_Porter
- Comments 9
- Last comment by Todd_Trimble
- Last Active May 2nd 2020

I have split off ordinal sum from the entry on joins as it is needed in other entries as well. I have not revised the entry just doing a cut and paste, so it needs more work!

- Discussion Type
- discussion topicDalitz decay
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 2nd 2020