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Created lexicographic order.
(also at wall crossing)
I am moving the following old query box exchange from orbifold to here.
old query box discussion:
I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely does not view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.
Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?
Urs Schreiber: please, go ahead. It would be appreciated.
end of old query box discussion
stub for T-fold
started a bare minimum at Poisson-Lie T-duality, for the moment just so as to have a place to record the two original references
added a few lines and original references to supersymmetry breaking.
finally cross-linked Landau-Ginzburg model with TCFT and added a corresponding reference,
prompted by this Physics.SE question
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 -limits where 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. =–
added the statement that categories with finite products are cosifted (here). Since this is referenced or used in a few other entries, I will give the statement and its proof a stand-alone entry now…
One day I hope to find the time to make universe a disambiguation page that also points to the physical meaning of the term.
For the time being: just a stub for observable universe, containing nothing but one link to a video. But one worth linking to.
Made a start on taut functor. Mike, I mentioned your work with Cruttwell on generalized multicategories in a section on applications.
removed the ”redirects BV quantization” command. given that there is already BV-BRST formalism, is this page still necessary?
This is a bare list of references, to be !include-ed into the References-lists of relevant entries (such as at anyon, topological order, fusion category, unitary fusion category, modular tensor category).
There is a question which I am after here:
This seems to be CMT folklore, as all authors state it without argument or reference.
Who is really the originator of the claim that anyonic topological order is characterized by certain unitary braided fusions categories/MTCs?
Is it Kitaev 06 (which argues via a concrete model, in Section 8 and appendix E)?
added pointer to
started a stubby nPOV-description at the beginning of BV-BRST formalism
somebody please stop me, though, because I urgently need to be doing something else... :-)
couple of pointers
Kevin Costello. Renormalisation and the Batalin-Vilkovisky formalism (2007). (arXiv:0706.1533).
Pavel Mnev. Discrete BF theory (2008). (arXiv:0809.1160).
Created:
Elliott Mendelson was a mathematician at CUNY. He got his PhD degree in 1955 from Cornell University, advised by J. Barkley Rosser.
An expository account of the NBG set theory:
An AnonymousCoward started NBG last month.
stub for dark matter
in analogy to what I just did at classical mechanics, I have now added some basic but central content to quantum mechanics:
Quantum mechanical systems
States and observables
Spaces of states
Flows and time evolution
Still incomplete and rough. But I have to quit now.
Created stub for the Reeh-Schlieder Theorem. this is needed a lot in AQFT, mostly as an axiom/a precondition for other statements. I intend to add a proof for the vacuum representation: this is often cited as “well known”, but it is not that easy to find a full and consistent one in the literature.
adding references
Ming Ng, Steve Vickers, Point-free Construction of Real Exponentiation, Logical Methods in Computer Science, Volume 18, Issue 3 (August 2, 2022), (doi:10.46298/lmcs-18(3:15)2022, arXiv:2104.00162)
Steve Vickers, The Fundamental Theorem of Calculus point-free, with applications to exponentials and logarithms, (arXiv:2312.05228)
Anonymouse
Adding reference
Anonymouse
Added a recent reference on Peirce’s Gamma graphs for modal logic. This describes his first approach via broken cuts rather than the later tinctured sheet approach. I keep meaning to see if there’s anything in the latter close to LSR 2-category of modes approach.
According to the broken-cut method, possibility is broken cut surrounding solid cut, while necessity is solid cut surrounding broken cut. Since solid cut is negation, broken cut signifies not-necessarily. Easy to see as the same pattern of three cuts, etc.
In the Alpha case, we’re to think of negated propositions as though written elsewhere on another sheet (or the back of the sheet). There seems to be a three-dimensionality to the graphs, e.g., the conditional as like a tube from one sheet to another, Wikipedia. I gather his later ideas on tinctured graphs had this idea of being inscribed on different sheets.
I have added to algebra for an endofunctor a remark on the relation to algebras over free monads. While I think that’s pretty obvious, I notice that a) recently somebody has blogged about that here, b) here it says that it’s not true :-) (but I think it’s not meant to be read that way).
brief category:people-entry, for the time being just to satisfy a link requested at Wiles’ proof of Fermat’s last theorem
Saw him deadlinked on Wiles’ proof of Fermat’s last theorem. He’s definitely important enough for an own page.
Corrected typo (“havin”) and added two papers from Iwasawa theory and function field analogy.
Added paper from orthogonal calculus:
Copied paper about algebraic surfaces from new page about Oscar Zariski:
Copied paper about algebraic surfaces from new page about Oscar Zariski:
Copied paper about algebraic surfaces from new page about Oscar Zariski:
Created new page for Takaaki Nomura and linked it on GUT (together with a forgotten link to Yutaka Hosotani above), Higgs field, Randall-Sundrum model, SO(12), Z’-boson, flavour anomaly and gauge-Higgs unification.
Saw him deadlinked on contributors to algebraic geometry. He’s definitely important enough for an own page.
Saw him deadlinked on contributors to algebraic geometry. He’s definitely important enough for an own page.
Saw him deadlinked on contributors to algebraic geometry. He’s definitely important enough for an own page.
took the liberty of changing at ind-object the links that previously pointed to finitely presentable object directly to compact object.
It would be nice if we could eventually expand on the query-box discussion at finitely presentable object, but currently there seems to be no point in directing to this entry instead of “compact object” if just commutitivity with colimits matters.
Did we really not have continuous poset?
a bare list of references, to be !include-ed into the References-sections of relevant entries, such as at Skyrmion and at quantum hadrodynamics
Added another paper from Fukaya category.