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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)
added doi-link to
I found the definition of a scheme to be slightly unclear/insufficiently precise at one point, so I have tweaked things slightly, and added more details. Indeed, it is quite common to find a formulation similar to ’every point has an open neighbourhood isomorphic to an affine scheme’, whereas I think it important to be clear that one does not have the freedom to choose the sheaf of rings on the local neighbourhood, it must be the restriction of the structure sheaf on .
Auke Booij’s thesis Analysis in univalent type theory as well as the HoTT book explicitly defines an ordered field to have an lattice structure on the underlying commutative ring, which is different from the definition of an ordered field in the nlab article, where such a condition is missing. (by lattice I mean unbounded lattice, or what some people call pseudolattices)
However, there are no references in the current nlab article on ordered fields showing that an ordered field doesn’t have a lattice structure in constructive mathematics. The basic definition lacking a lattice structure was already written in 2010 in the first revision of the article by Toby Bartels, and the other editors of the article, Todd Trimble and a few anonymous editors from earlier this year, all accepted the basic definition provided by Toby Bartels, since it hasn’t been modified since the first revision. So if they are still around I would like them or somebody else to provide references from the mathematical literature justifying that ordered fields do not necessarily have a lattice structure, or prove that every ordered field as currently defined has a compatible lattice structure. Otherwise I’ll insert the lattice structure into the definition.
I have split off complex projective space from projective space and added some basic facts about its cohomology.
rediscovered this ancient entry. Added publication data for:
that has become available meanwhile :-)
also added pointer to:
I am working on the entry supergravity C-field. On the one hand I am in the process of adding in more on the DFM model. On the other I am describing how to reformulate aspects of this in terms of infinity-Chern-Weil theory (this with Domenico Fiorenza and Hisham Sati behind the scenes).
Not done yet, so beware.
expanded and polished Kalb-Ramond field. In particular I added more references.
added references and cross-linked with electromagnetic potential (these two entries probably ought to be merged)
added to G2 the definition of as the subgroup of that preserves the associative 3-form.
Added
the first now of ’Selected writings’.
started M-theory on G2-manifolds
added an Idea-section to coherence theorem for monoidal categories just with the evident link-backs and only such as to provide a minimum of an opening of the entry
Inspired by the discussion at directed n-graph and finite category, added some examples and further explanation to computad.
started a minimum at writer comonad
For some time now I’ve been bothered by an implicit redundancy spanned by the articles nice category of spaces and convenient category of topological spaces. I would like the latter to have a more precise meaning and the former to be something more vague and flexible. I have therefore been doing some rewriting at the former. But if anyone disagrees with the edits, please let’s discuss this here.
I have removed a query box:
+– {: .query} I’m not sure that we really want to use the terminology that way, but Ronnie already created that page, so I’m linking these together. —Toby =–
At simplex I have accompanied the definition of the cellular simplex with that of the topological simplex.
Charles Waldo Rezk is a mathematician at the University of Illinois Urbana–Champaign.
He got his PhD degree in 1996 at MIT, advised by Michael J. Hopkins.
His PhD students include Nathaniel Stapleton and Nima Rasekh.
This is a bare list of references, to be !include-ed into relevant entries (such as string phenomenology, heterotic string and GUT), for ease of keeping these entry’s bibliographies in sync
Added pointer to section 7 of
starting some minimum, cross-linking with quaternion-Kähler manifold and Sp(n).Sp(1)
starting something, for the moment just so as to record that
there is a homeomorphism
between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.
Asked a question at natural transformation.
had occasion to create dual vector space.
I added to initial object the theorem characterizing initial objects in terms of cones over the identity functor.
for the Café-discussion I added to zero object the details of the proof that in a -enriched category every terminal or initial object is zero.
In the course of this I did a bit of brushing-up of a bunch of related entries. For instance at pointed set I made the closed monoidal structure on manifest, etc.