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Edit to: standard model of particle physics by Urs Schreiber at 2018-04-01 01:15:37 UTC.
Author comments:
added textbook reference
cross-linked with Euler form and added these pointers:
Discussion of Euler forms (differential form-representatives of Euler classes in de Rham cohomology) as Pfaffians of curvature forms:
{#MathaiQuillen86} Varghese Mathai, Daniel Quillen, below (7.3) of Superconnections, Thom classes, and equivariant differential forms, Topology Volume 25, Issue 1, 1986 (10.1016/0040-9383(86)90007-8)
{#Wu05} Siye Wu, Section 2.2 of Mathai-Quillen Formalism, pages 390-399 in Encyclopedia of Mathematical Physics 2006 (arXiv:hep-th/0505003)
Hiro Lee Tanaka, Pfaffians and the Euler class, 2014 (pdf)
{#Nicolaescu18} Liviu Nicolaescu, Section 8.3.2 of Lectures on the Geometry of Manifolds, 2018 (pdf, MO comment)
I’ve added to reflexive graph a definition of the free category of a reflexive quiver.
That page needs some reorganization because everything now said there is about reflective quivers, and not say about reflective undirected simple graphs.
Maybe free category also also needs touching up and maybe a link to reflective graph. I don’t know how to justify that the paths in the free category don’t contain identity edges.
a bare list of references, to be !include-ed into the References-sections of relevant entries (such as supersymmetry and solid state physics) for ease of synchronization
a bare list of bibitems, to be !include-ed into the References-section of relevant entries (such as fractional quantum Hall effect and Laughlin wavefunctions), for ease of synchronization
I gave CW-pair its own entry.
have created an entry Khovanov homology, so far containing only some references and a little paragraph on the recent advances in identifying the corresponding TQFT. I have also posted this to the nCafé here, hoping that others feel inspired to work on expanding this entry
have created geometric infinity-stack
gave Toën’s definition in detail (quotient of a groupoid object in an (infinity,1)-category in TAlgop∞Spec↪Sh∞(C) ) and indicated the possibility of another definition, along the lines that we are discussing on the nCafé
added to quantum anomaly
an uncommented link to Liouville cocycle
a paragraph with the basic idea of fermioninc anomalies
the missing reference to Witten’s old article on spin structures and fermioninc anomalies.
The entry is still way, way, stubby. But now a little bit less than a minute ago ;-
the table didn’t have the basic examples, such as Gelfand duality and Milnor’s exercise. Added now.
(Hi, I’m new)
I added some examples relating too simple to be simple to the idea of unbiased definitions. The point is that we often define things to be simple whenever they are not a non-trivial (co)product of two objects, and we can extend this definition to cover the “to simple to be simple case” by removing the word “two”. The trivial object is often the empty (co)product. If we had been using an unbiased definition we would have automatically covered this case from the beginning.
I also noticed that the page about the empty space referred to the naive definition of connectedness as being
“a space is connected if it cannot be partitioned into disjoint nonempty open subsets”
but this misses out the word “two” and so is accidentally giving the sophisticated definition! I’ve now corrected it to make it wrong (as it were).
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
brief category:people-entry for hyperlinking references at equivariant principal bundle
category: people page for the reference
Anonymouse
category: people page for the reference
Anonymouse
I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of “continuation-passing” transform.
I’ve been inactive here for some months now; I hope this will significantly change soon.
I have written a stubby beginning of iterated monoidal category, with what is admittedly a conjectural definition that aims to be slick. I am curious whether anyone can help me with the following questions:
Is the definition correct (i.e., does it unpack to the usual definition)? If so, is there a good reference for that fact?
Assuming the definition is correct, it hinges on the notion of normal lax homomorphism (between pseudomonoids in a 2-category with 2-products). Why the normality?
In other words (again assuming throughout that the definition is correct), it would seem natural to consider the following type of iteration. Start with any 2-category with 2-products C, and form a new 2-category with 2-products Mon(C) whose 0-cells are pseudomonoids in C, whose 1-cells are lax homomorphisms (with no normality condition, viz. the condition that the lax constraint connecting the units is an isomorphism), and whose 2-cells are lax transformations between lax homomorphisms. Then iterate Mon(−), starting with C=Cat. Why isn’t this the “right” notion of iterated monoidal category, or in other words, why do Balteanu, Fiedorowicz, Schwänzel, and Vogt in essence replace Mon(−) with Monnorm(−) (where all the units are forced to coincide up to isomorphism)?
Apologies if these are naive questions; I am not very familiar with the literature.
a bare minimum, for the moment just so as to satisfy links from graded modality
I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?
copied over the homotopy-theoretic references from modal type theory to here.