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added to the Properties-section at Hopf algebra a brief remark on their interpretation as 3-vector spaces.
I started an idea section at transgression, but it could probably use some going over by an expert. I hope I didn’t mess things up too badly. I was reading Urs’ note on “integration without integration” on the train ride home and fooled myself into thinking I understood something.
By the way, this reminded me of a discussion we had a while back
Started this, following this comment.
I wrote a little piece at general covariance on how to formalize the notion in homotopy type theory. Just for completeness, I also ended up writing a little blurb at the beginning about the genera idea of general covariance.
added publication details for this reference:
and am copying it over to compactly generated topological space, too
I have added to orthogonal factorization system
in the Definition-section three equivalent explicit formulations of the definition;
in the Properties-section the statement of the cancellability property.
Wanted to add more (and to add the proofs). But have to quit now. Maybe later.
I treid to clean up Whitehead tower a bit:
I rewrote and expanded the Idea/Definition part.
Then I moved David Roberts' material that was there to the appropriate section at the new Whitehead tower in an (infinity,1)-topos. (There I tried to add some introductory remarks to it but will try to further highlight David's results here in a moment).
At Whitehead tower I left just a new section that says that there is a notion of Whitehead towers in more general contexts with a pointer to Whitehead tower in an (infinity,1)-topos
I finally gave the Connes-Lott-Chamseddine-Barrett model its own entry. So far it contains just a minimum of an Idea-section and a minimum of references.
This was prompted by an exposition on PhysicsForums Insights that I wrote: Spectral standard model and String compactifications
tried to polish one-point compactification. I think in the process I actually corrected it, too. Please somebody have a close look.
as mentioned in another thread, I have expanded the Idea-section at polarization in order to highlight the relation to canonical momenta (which I also edited accordingly).
started an Examples-section at geometric quantization
there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).
I have added a remark on this in the (g−2)-entry here and also at quantum gravity here.
I have been expanding and polishing the entry Heisenberg group.
This had existed in bad shape for quite a while, but now it’s maybe getting into better shape.
I tried to spend some sentences on issues which I find are rarely highlighted appropriately in the literature. So there is discussion now of the fact that
there are different Lie groups for a given Heisenberg Lie algebra,
and the appearance of an “i” in [q,p]=i may be all understood as not picking the simply conncted ones of these;
I also added remarks on the relation to Poisson brackets, and symplectomorphisms.
In this context: either I am dreaming, or there is a mistake in the Wikipedia entry Poisson bracket - Lie algebra.
There it says that the Poisson bracket is the Lie algebra of the group of symplectomorphisms. But instead, it is the Lie algebra of a central extension of the group of Hamiltonian symplectomorphisms.
I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:
created sections
added to group extension a section on how group extensions are torsors and on how they are deloopings of principal 2-bundles, see group extension – torsors
Initial stub to record some references. Wanted by type theoretic model category
The entry test category which I wrote some time ago, came into the attention of Georges Maltsiniotis who kindly wrote me an email with a kind praise on nlab and noting that his Astérisque treatise on the topic of Grothendieck’s homotopy theory is available online on his web page and that the Cisinski’s volume is sort of a continuation of his Astérisque 301. Georges also suggested that we should emphasise that a big part of the Pursuing Stacks is devoted to the usage of test categories, so I included it into the bibliography and introductory sentence. I hinted to Georges that when unhappy with a state of an nlab entry he could just feel free to edit directly.
Have added to pushout-product the statement (here) that pushout product □ of I1-cofibrations with I2-cofibrations lands in (I1□I2)-cofibrations; and (here) the example of pushout products of the inclusions Sn−1↪Dn. Both without proof for the moment.
Added a paper:
I fixed a link to a pdf file that was giving a general page, and not the file!
the book Monoidal Functors, Species and Hopf Algebras is very good, but still being written. Clearly the current link under which it is found on the web is not going to be the permanent link. So I thought it is a bad idea to link to it directly. Instead I created that page now which we can reference then from nLab entries. When the pdf link changes, we only need to adapt it at that single page.
created nilradical
I felt that we had too many gray links to metalanguage, so I gave it a try. But I don’t really have the leisure for it now and not the expertise anyway. Experts please feel invited to take apart what I wrote there and replace with it something better.