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at the beginning of ring I have spelled out a more explicit definition. Also added the examples of rings on cyclic groups to explain the origin of the word “ring”.
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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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added an Idea-section to Mackey functor (which used to be just a list of references). Also added more references.
I worked on brushing up (infinity,1)-category a little
mostly I added in a section on homotopical categories, using some paragraphs from Andre Joyal's message to the CatTheory mailing list.
in this context I also rearranged the order of the subsections
I removed in the introduction the link to the page "Why (oo,1)-categories" and instead expanded the Idea section a bit.
added a paragraph to the beginning of the subsection on model categories
added the new Dugger/Spivak references on the relation between quasi-cats and SSet-cats (added that also to quasi-category and to relation between quasi-categories and simplicial categories)
Redirects also semantics (linguistics).
added to identity type a mentioning of the alternative definition in terms of inductive types (paths).
added to inter-universal Teichmüller theory a pointer to the recent note
(Though after reading I am not sure if that note helps so much.)
a bare list of references, to be !include-ed into the lists of references of relevant entries (at quantum hall effect and noncommutative geometry, maybe also at matrix model), for ease of synchronizing
a bare list of references, to be !include-ed into the References-lists of relevant entries (such as at anyon and quantum Hall effect) for ease of updating and synchronizing
I tried adding some material to framed link, but as in other recent edits (Dehn twist, Dehn surgery), my efforts might well make an expert smile indulgently. I do mean to – or someone else could – fix up or polish up the recent edit at Dehn surgery, which I’m not particularly happy with at the moment.
I added the definition and several references on higher dimensional knots under knot.
I have added to the References at double negation pointer to Andrej’s exposition:
which is really good. I have also added this to double negation transformation, but clearly that entry needs some real references, too.
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 a link to Todd’s nice page on free cartesian category.
I did not change anything, I would not like to do it without Urs’s consent and some opinion. The entry AQFT equates algebraic QFT and axiomatic QFT. In the traditional circle, algebraic quantum field theory meant being based on local nets – local approach of Haag and Araki. This is what the entry now describes. The Weightman axioms are somewhat different, they are based on fields belonging some spaces of distributions, and 30 years ago it was called field axiomatics, unlike the algebraic axiomatics. But these differences are not that important for the main entry on AQFT. What is a bigger drawback is that the third approach to axiomatic QFT if very different and was very strong few decades ago and still has some followers. That is the S-matrix axiomatics which does not believe in physical existence of observables at finite distance, but only in the asymptotic values given by the S-matrix. The first such axiomatics was due Bogoliubov, I think. (Of course he later worked on other approaches, especially on Wightman’s. Both the Wightman’s and Bogoliubov’s formalisms are earlier than the algebraic QFT.)
I would like to say that axiomatic QFT has 3 groups of approaches, and especially to distinguish S-matrix axiomatics from the “algebraic QFT”. Is this disputable ?
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.)
I added a note to compact closed category on the fact that the inclusion from compact closed categories into SMCCs has a left adjoint, pointing to an article by Day where he describes the free compact closed category over a closed symmetric monoidal category as a localization. Question: this left adjoint is not full, but I believe it is faithful – does anyone know how to prove that?
edited dualizable object a little, added a brief paragraph on dualizable objects in symmetric monoidal -categories
Added to group object the Yoneda-embedding-style definition and added supergroup to the list of examples.
same as in companion pair
Created descent morphism.
In adding links, I discovered that Euclidean-topological infinity-groupoid and separated (infinity,1)-presheaf use the phrase “descent morphism” to refer to the comparison functor mapping into the category of descent data. If no one has any objections, I would like to change this to avoid confusion, but I’m not sure what to change it to: would “comparison functor” be good enough?
I felt we needed a dedicated entry on model/category of models. So I started one. But just a puny stub so far.
I am working on an entry cohesive homotopy type theory.
This started out as material split off from cohesive (infinity,1)-topos, but is expanding now.
starting page on type theories with parametricity, as a separate article from the article on polymorphism.
Anonymouse
Adding reference
Anonymouse
stub for spin-statistics theorem. Just recording a first few references so far.
Added a reference of Robert Furber, Bart Jacobs at Giry monad.
I added the word “strict” here:
The theorem is then that the following are equivalent:
- is a strict Conduché functor.
- is exponentiable in the 1-category .
- is exponentiable in the strict 2-category .
because strict and weak Conduché functors are being distinguished in this article.
promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:
mentioned more relations to other concepts in the Idea-section;
added an Examples-section with a bunch of (classes of) examples;
added a list of references. Please add more if you can think of more!