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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
created Lie bialgebra, but so far just a comment on their quantization.
This is intended to continue the issues discussed in the Lafforgue thread!
I have added an idea section to Morita equivalence where I sketch what I perceive to be the overarching pattern stressing in particular the two completion processes involved. I worked with ’hyphens’ there but judging from a look in Street’s quantum group book the pattern can be spelled out exactly at a bicategorical level.
I might occasionally add further material on the Morita theory for algebraic theories where especially the book by Adamek-Rosicky-Vitale (pdf-draft) contains a general 2-categorical theorem for algebraic theories.
Another thing that always intrigued me is the connection with shape theory where there is a result from Betti that the endomorphism module involved in ring Morita theory occurs as the shape category of a ring morphism in the sense of Bourn-Cordier. Another thing worth mentioning on the page is that the Cauchy completion of a ring in the enriched sense is actually its cat of modules (this is in Borceux-Dejean) - this brings out the parallel between Morita for cats and rings.
created a stub for twisted differential cohomology and cross-linked a bit.
This for the moment just to record the existence of
No time right now for more. But later.
added some pointers:
Yves Félix, Stephen Halperin, Jean-Claude Thomas, p. 142 in: Rational Homotopy Theory, Graduate Texts in Mathematics, 205, Springer-Verlag, 2000 (doi:10.1007/978-1-4613-0105-9)
Luc Menichi, Section 1.2 in: Rational homotopy – Sullivan models, IRMA Lect. Math. Theor. Phys., EMS (arXiv:1308.6685)
I looked at real number and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:
A real number is something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form a number field, denoted . The underlying set is the completion of the ordered field of rational numbers: the result of adjoining to suprema for every bounded subset with respect to the natural ordering of rational numbers.
The set of real numbers also carries naturally the structure of a topological space and as such is called the real line also known as the continuum. Equipped with both the topology and the field structure, is a topological field and as such is the uniform completion of equipped with the absolute value metric.
Together with its cartesian products – the Cartesian spaces for natural numbers – the real line is a standard formalization of the idea of continuous space. The more general concept of (smooth) manifold is modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (see spacetime), or at least in classical physics. See at geometry of physics for more on this.
have added to Topos in the section on limits of toposes the description of the pullback of toposes by pushout of their sites of definition.
added this pointer:
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 created a page for Riemannian metric based on a "blog post": http://deltaepsilons.wordpress.com/2009/10/27/riemannian-metrics-and-connections/ and a suggestion of Urs Schreiber.
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<p>created <a href="https://ncatlab.org/nlab/show/nonabelian+group+cohomology">nonabelian group cohomology</a></p>
<p>the secret title of this entry is "Schreier theory done right". (where "right" is right from the <a href="https://ncatlab.org/nlab/show/nPOV">nPOV</a>)</p>
<p>this is the first part of the answer to</p>
<blockquote>
What is going on at <a href="https://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology">nonabelian Lie algebra cohomology</a>?
</blockquote>
<p>The second part of the answer is the statement:</p>
<blockquote>
The same.
</blockquote>
<p>;-)</p>
<p>I'll expand on that eventually.</p>
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Mike Stay kindly added the standard QM story to path integral.
I changed the section titles a bit and added the reference to the Baer-Pfaeffle article on the QM path integral. Probably the best reference there is on this matter.
added to string theory FAQ two new paragraphs:
Prompted by the MO discussion
added to S-matrix a useful historical comment by Ron Maimon (see there for citation)
added pointer to yesterday’s
Added link to Feynman polytope and the Arkani-Hamed, Hillman and Mizera reference
Theresa
Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron
at associative operad I have made explict the links to symmetric operad and planar operad, as need be.
starting something, but not much here yet.
Eventually I’d like to make a linked cube diagram of flavors of Hall effects (quantum, anomalous, fractional). Something like this was attempted in Figure 1 of
but maybe we can improve on that…
I have considerably expanded the entry sigma-model and will probably continue to do so in small steps in the nearer future (with interruptions). This goes in parallel with a discussion we are having on the Café here.
added these two pointers:
Karen Uhlenbeck, notes by Laura Fredrickson, Equations of Gauge Theory, lecture at Temple University, 2012 (pdf)
Simon Donaldson, Mathematical uses of gauge theory (pdf)
(if anyone has the date or other data for the second one, let’s add it)
In light of people such as Taichi Uemura using assemblies in areas unrelated to realizability, I’ve decided to split off the text on assemblies and its category from realizability topos to its own article.
George Harrison
the analogue of circle type localization but for the interval type. Comes with a proof that interval type localization implies the J-rule
Anonymouse
stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)
After scanning a bunch of literature, my favorite survey of the Adams spectral sequence is now this gem here:
starting page on Cyrille Chenavier for the sake of a reference at associative operad
Abe
added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)
added the same statement also at Fulton-MacPherson operad
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!
added more references to 2-spectral triple (as far as I can see Jürg Fröhlich with his students was the first to try to formalize this to some extent)
a bare list of references (for articles considering “unstable” or “fragile” classification of topological phases of matter, not in K-theory but by the non-abelian cohomology classified by finite-dimensional Grassmannians or flag manifolds)
to be !include-ed into the list of references at relevant entries, for ease of synchronizing
a bare list of references, to be !include-ed into the References-section of relevant entries (such as at braid group representation and at semi-metal).
Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited
I decided it would be a good idea to split off realizability topos into a separate entry (it had been tucked away under partial combinatory algebra). I’ve only just begun, mainly to get down the connection with COSHEP. A good (free, online) reference is Menni’s thesis.
Created sound doctrine as a stub to record relevant references.