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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added publication data (notably the doi:10.1007/BFb0084585) and some formatting
in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity
Started 12-dimensional supergravity following some discussion with Urs.
Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).
added illustrating diagram to transfinite composition
I also renamed the resulting composite morphism into . Hope I did this consistently.
created quick stub for framed bicategory
but my machine's battery will die any second now...
I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.
Added idempotent monoidal functor.
split off strict initial object from initial object (in order to be able to point to it directly from within proofs elsewhere)
I made the former entry "fibered category" instead a redirect to Grothendieck fibration. It didn't contain any addition information and was just mixing up links. I also made category fibered in groupoids redirect to Grothendieck fibration
I also edited the "Idea"-section at Grothendieck fibration slightly.
That big query box there ought to be eventually removed, and the important information established in the discussion filled into a proper subsection in its own right.
Added the Yoneda-embedding way to talk about group objects and hence supergroups.
added pointer to Belopolsky97b etc., regarding “picture number” induced by a choice of integral top-forms.
Somebody from the technical team kindly alerted me that we have a full .mov
copy of the video recording of Kapranov 2013 sitting on the nLab server – which is strange (but also lucky), does anyone know/remember how this came to be?
In trying to understand what’s going on, I noticed that the relevant YouTube link at Kapranov 2013 had died (“private”) as had my original video link from comment #5 in the original thread. Also the links to the hosting conference had meanwhile rotted away.
I have now
recovered the conference links via the WaybackMachine,
added the link to our local copy of the video recording
and am also uploading the video to YouTube.
Am propagating these edits also to other entries where Kapranov’s talk is referenced, such as at Mikhail Kapranov and at spectral super-scheme.
added ISBN:978-0-8218-2014-8
pointer
added pointer to this obituary:
A stub, for the moment just to have a place for recording a couple of references (which were previously at fusion category.
stub for spin-statistics theorem. Just recording a first few references so far.
created directed homotopy type theory
To support mentioning weak wreath product in a parallel discussion with Urs, I created a stub for weak bialgebra with redirect weak Hopf algebra.
in analogy to what I just did at classical mechanics, I have now added some basic but central content to quantum mechanics:
Quantum mechanical systems
States and observables
Spaces of states
Flows and time evolution
Still incomplete and rough. But I have to quit now.
a stub, for the moment just to make some cross-links work (such as with topological order and topological entanglement entropy)
added pointer to:
created worldline formalism to go with this Physics.SE answer
I expanded perfect infinity-stack a little. But this deserves further polishing and expanding.
I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.
I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.
In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes
The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.
one more from Meissner & Nicolai, last week:
I moved the definition of promonoidal categories from Day convolution to promonoidal category, and expanded on it a bit.
New entry representable morphism, in the sense of Grothendieck school. The notion is used at closed immersion of schemes where I just made some changes.
Following discussion in some other threads, I thought one should make it explicit and so I created an entry
Currently this contains some (hopefully) evident remarks of what “dependent linear type theory” reasonably should be at least, namely a hyperdoctrine with values in linear type theories.
The entry keeps saying “should”. I’d ask readers to please either point to previous proposals for what “linear dependent type theory” is/should be, or criticise or else further expand/refine what hopefully are the obvious definitions.
This is hopefully uncontroversial and should be regarded an obvious triviality. But it seems it might be one of those hidden trivialities which deserve to be highlighted a bit more. I am getting the impression that there is a big story hiding here.
Thanks for whatever input you might have.
stub for jet bundle
An edit to normed ring is being discussed in another thread, here.
added pointer to:
added to Cartan connection
definition
a standard reference
a standard example
I see super-Cartan geometry is taking shape. Will Clifford algebras make an appearance in the The super-Klein geometry: super-Minkowski spacetime section?
Is there a higher super-Cartan way of thinking about what is at 3-category of fermionic conformal nets, about the String 2-group and superstrings, as here about the spin group and fermions.
added ISBN:9783540125464
I am changing the page title – this used to be “A first idea of quantum field theory”, which of course still redirects. The “A first idea…” seemed a good title for when this was an ongoing lecture that was being posted to PhysicsForums. I enjoyed the double meaning one could read into it, but it’s a bad idea to carve such jokes into stone. And now that the material takes its place among the other chapters of geometry of physics, with the web of cross-links becoming thicker, the canonical page name clearly is “perturbative quantum field theory”.
added pointer to these two recent references, identifying further -algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:
Markus B. Fröb, Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories (arXiv:1803.10235)
Alex Arvanitakis, The -algebra of the S-matrix (arXiv:1903.05643)
finally added the actual definition, !include
-ed from Knizhnik-Zamolodchikov-Kontsevich construction – definition (as per the discussion here)
renaming page to the one used in the Stacks reference, parallel with Artinian ring.
Anonymous
Created W-type.