Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
created a “category: reference”-page The Stacks Project
I have only now had a closer look at this and am impressed by the scope this has. Currently a total of 2288 pages. It starts with all the basics, category theory, commutative algebra and works its way through all the details to arrive at algebraic stacks.
So besides my usual complaint (Why behave as if there are not sites besides the usual suspects on and either give a general account or call this The Algebraic Stacks Project ? ) I am enjoying seeing this. We should have lots of occasion to link to this. Too bad that this did not start out as a wiki.
Added this reference
stub for type II geometry
created a currently fairly empty entry quantum measurement, just so as to have a place where to give a commented pointer to the article
I needed an entry to be able to point to which collects pointers to the various entries on “dualities” in string theory. So I created one: duality in string theory.
I have edited at Tychonoff theorem:
tidied up the Idea-section. (Previously there was a long paragraph on the spelling of the theorem before the content of the theorem was even mentioned)
moved the proofs into a subsection “Proofs”, and added a pointer to an elementary proof of the finitary version, here
Notice that there is an ancient query box in the entry, with discussion between Todd and Toby. It would be good to remove this box and turn whatever conclusion was reached into a proper part of the entry.
At then end of the entry there is a line:
More details to appear at Tychonoff theorem for locales
which however has not “appeared” yet.
But since the page is not called “Tychonoff theorem for topological spaces”, and since it already talks about locales a fair bit in the Idea section, I suggest to remove that line and to simply add all discussion of localic Tychonoff to this same entry.
Started lift.
weak factorization system has redirects from: lifting property, right lifting property, left lifting property, lifting problem, lifting problems.
Would it be better to have these redirect to lift?
a bare subsection with a list of references, to be !include
-ed at super Riemann surface and at moduli space of super Riemann surfaces, for ease of synchronization
added pointer to today’s
For the purposes of negative thinking, it may be useful to recognise that every -category has a -morphism, which is the source and target of every object. (In the geometric picture, this comes as the -simplex of an augmented simplicial set.)
Jonathan Arnoult has pointed out on CT Zulip that this is misleading: it sounds like it implies that every -category is monoidal! And John Baez pointed out that the analogy to augmented simplicial sets fails because in an augmented simplicial set each 0-simplex has only one face, rather than a separate “source” and “target” that are both the same -simplex.
I suggest we just remove this paragraph and the query box following it, since I can’t think of a way to rephrase it that would be more helpful than unhelpful. But I’m open to other suggestions.
created quick stub for framed bicategory
but my machine's battery will die any second now...
I have added to string theory a new section Critical strings and quantum anomalies.
Really I was beginning to work on a new entry twisted spin^c structure (not done yet) and then I found that a summary discussion along the above lines had been missing.
for discussion at geometry of physics I needed to be able to point to principle of extremal action, so I created a little entry.
I added a reference on Gabriel filters on quantales.
Very strange: version one on show had a reference on Etendues (entered by T. Holder), but when I clicked edit there was none in the edit window, just in show window. I edited and one can not see it in any history, nowhere. So there was something in show cache from 2014 which is not recorded in any history edit.
starting something on the concept introduced in
Sergei O. Ivanov, Roman Mikhailov: A higher limit approach to homology theories, Journal of Pure and Applied Algebra 219 6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]
Sergei O. Ivanov, Roman Mikhailov: Higher limits, homology theories and -codes, in: Combinatorial and Toric Homotopy, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]
but for the moment there is little more than these references
Expanded dinatural transformation a little with examples and references.
I gave Fourier-Mukai transform a bit of an Idea-section. It overlaps substantially with the Definition section now, but I thought one needs to say the simple basic idea clearly in words first. Also added a few more pointers to literature.
I am giving Modern foundations for stable homotopy theory a category:reference entry.
First thing I did was to brush-up the list of references at symmetric smash product of spectra. Then I copied over the nicely to-the-point History-paragraph to a new section stable homotopy theory – history.
have now spelled out at Tor in simple terms how is a torsion group, so far for the case that is finite.
added to equalizer statement and proof that a category has equalizers if it has pullbcks and products
I have added
and added publication details to
and grouped together more discernibly the references on operator-algebraic entropy
added at core the remark that the core is right adjoint to the forgetful functor .
felt the desire to have an entry on the general idea (if any) of synthetic mathematics, cross-linking with the relevant examples-entries.
This has much room for being further expanded, of course.
The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.
Adding reference
Anonymous
starting a category:reference
-entry.
Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at Handbook of Quantum Gravity and similar entries).
I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.
Have added pointer to:
(but I haven’t more than skimmed it and don’t mean to endorse it).