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stub for N=4 D=3 super Yang-Mills theory…
… for the moment just so as to be able to reference the literature on the flavor of S-duality needed at symplectic duality.
added pointer to the first known examples:
Daniele Amati, Ctirad Klimčík, Nonperturbative computation of the Weyl anomaly for a class of nontrivial backgrounds, Phys. Lett. B, 219:443–447, 1989 (spire:269390, 10.1016/0370-2693(89)91092-7)
Gary Horowitz, Alan R. Steif, Spacetime singularities in string theory, Phys. Rev. Lett. 64, 260 1990 (doi:10.1103/PhysRevLett.64.260)
I understood that the old terminology was ’projective system’, and ’projective limit’ refereed to the limit of a projective system. Can anyone confirm that? if I am right the present entry is slightly incorrect, but this needs checking first before changing it.
brief category:people-entry for hyperlinking references at CW complex
I edited The Joy of Cats to link to metacategory and to disambiguate quasicategory, as twice now someone on MO has used the term ’quasicategory’ to talk about (very) large categories. This way, if people find the book using the nLab page they are forewarned.
I also edited quasicategory to move the terminological warning up to the idea section where it is immediately visible, rather than in the second section, below the definition.
tried to improve the entry coproduct a little
added pointer to:
I have added to coequalizer basic statements about its relation to pushouts.
In the course of this I brought the whole entry into better shape.
added to equalizer statement and proof that a category has equalizers if it has pullbcks and products
added a Properties-section to pullback
I wrote out a proof that geometric realization of simplicial sets valued in compactly generated Hausdorff spaces is left exact, using essentially the observation that simplicial sets are the classifying topos for intervals, combined with various soft topological arguments. I left a hole to be plugged, that geometric realizations are CW complexes. I also added a touch to filtered limit, and removed a query of mine from triangulation.
I wanted a “pretty proof” for this result on geometric realization, centered on the basic topos observation (due to Joyal). I was hoping Johnstone did this himself in his paper on “a topological topos”, but I couldn’t quite put it together on the basis of what he wrote, so my proof is sort of “homemade”. I wouldn’t be surprised if it could be made prettier still. [Of course, “pretty” is in the eye of the beholder; mainly I want conceptual arguments which avoid fiddling around with the combinatorics of shuffle products (which is what I’m guessing Gabriel and Zisman did), decomposing products of simplices into simplices.]
The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:
Just the bare statements so far.
am clearing this duplicate page and merging into Robert A. Wilson
brief category:people-entry for hyperlinking references (at perturbative quantum field theory and maybe elsewhere)
brief category:people-entry for hyperlinking references (at perturbative quantum field theory and maybe elsewhere)
I have further expanded the Idea-section and the list of commented references at perturbative quantum field theory.
(Not proof-read yet, need to run to catch a train.)
brief category:people-entry for hyperlinking references at Lie group etc. and at Hall coherent state
discovered this neglected entry. Have at least added cross-link with coherent state and with Brian Charls Hall
brief category:people-entry for hyperlinking references at configuration space of points and Fulton-MacPherson compactification
created a simple entry ring object, just for completeness
started projective unitary group with some remarks on its obstruction theory. Also aded a comment with a pointerto this entry to lifting gerbe
mathematical physics with a slight distinction from physical mathematics which points to the same entry. The relation to theoretical physics has been discussed, but I am not sure yet if we should have theoretical physics as a separate entry so I do not put is as another redirect.
brief category:people-entry for hyperlinking references at mathematical phsyics
brief category:people-entry for hyperlinking references at Galois cohomology and elsewhere
<div>
<p>created <a href="http://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="http://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="http://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>
</div>
brief category:people-entry for hyperlinking references at Lie group cohomology
split off Lie group cohomology from group cohomology
started Galois cohomology
am giving this its own category:reference-entry, for better hyperlinking
Have done the same for Groupprops
am giving this a category:reference-entry, too, for better hyperlinking
Will do the same for GroupNames
created Einstein manifold
(for the moment only to record the example of weak -manifolds…)
brief category:people-entry for hyperlinking references at asymptotic safety
gave geometric algebra an Idea-section
I requested some more details at strict 2-category. It would be nice to have something describing how objects are categories, morphisms are ??? satisfying ???, 2-morphisms are ??? satisfying ???.
I'm sure all the details could be unwrapped from the simple statement "a strict 2-category is a Cat-category", but then I need to learn what an enriched category is first and then I need to see how that works in the case of Cat-enriched category. Soon, I feel overwhelmed. A strict 2-category is probably not THAT hard to understand explicitly.
for completeness, to go with strict 2-category and (2,1)-category
Added this
and upgrade of a previous paper from “a” to “all”.
Added original reference
and example of Church monoids
brief category:people-entry for hyperlinking references at group cohomology etc.
Finally splitting this off from lattice QCD in order to record some references. Gave it a rough Idea-section, but this remains a stub.