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I tried to prettify the entry topological space a bit more:
made an attempt at adding an Idea-section (feel free to work on that, it’s just a quick idea motivated more from the desire to have such a section at all than from an attempt to do it any justice).
collected the three Definition-sections to subsections of a single Definition-section
polished and expanded the Standard definition section.
A stub, to make links work at Wheeler superspace
Wikipedia has a nice article on quantum operations.
The nLab also had a page quantum operations and channels (cache bug?), but I’ve renamed this to simply quantum operation since a quantum channel seems to be nothing but a quantum operation when viewed from the perspective of quantum information theory. Eventually, this page might need some disambiguation since there may be several uses of the term, but for now I think it is “ok”.
I think this page can be cleaned up. I started, but don’t think I will be able to finish.
In particular, there is some background material that might be better on separate pages. I’ll continue trying to clean things up, but family might be calling soon and I’ll need to run quickly whatever state it is in.
I also made the simple statement
In quantum mechanics, a quantum operation is a morphism in the category of density matrices
at the beginning of the Idea section motivated by O’Loan’s comment
A quantum channel is a mapping which sends density matrices to density matrices.
This seems innocent enough, but someone might check the statement. For one, I’ve never seen a category of density matrices, but the idea seems obvious enough. Maybe a word on density matrix would be good.
added pointer to today’s
have added some minimum of references (there were none before)
but I hope to find the time to put some actual content into the entry:
the sequence of exceptional tangent bundles used to be truncated, and the other day I saw (cf. nForum discussion here and here) how to complete it, using recent results.
a pdf note is now here (just 1 page)
Created reflexive coequalizer.
wrote an Idea-section at quantum field theory
created hyperring
stub (except for a brief remark on this being the gauge group in type I ST), for the moment just to fill the pattern at low dimensional rotation groups – table
am finally adding references here, such as
will add these also to lattice gauge theory as far as there is overlap
Todd,
when you see this here and have a minute, would you mind having a look at monoidal category to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?
Thanks!
Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Added redirect for “E9” at the bottom of the page.)
a bare list of references, to be !include-ed into the References-lists of relevant entries (inductive type, inductive familiy, inductive-recursive family, calculus of inductive constructions)
this list includes a polished-up version of
all the references previously listed at inductive familiy in the section “History” (due to revisions by Bas Spitters)
further references previously listed at inductive-recursive type
and some more
created traced monoidal category with a bare minimum
I would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.
Added:
The large cardinal strength of the weak Vopěnka principle is discussed in
The following paper shows that weak Vopěnka’s principle is indeed weaker than Vopěnka’s principle:
Created new article for Bi-Yang-Mills equation. (The english and german Wikipedia article are now also available.)
Created new article for F-Yang-Mills equation. (The english and german Wikipedia article are now also available.)
copied article from the michaelshulman wiki at functor comprehension principle (michaelshulman) to the nlab wiki.
C. Silva
I am touching various entries related to equivariant stable homotopy theory, adding basics from the literature. For instance I briefly added to G-spectrum the basic definition via indexing on a universe, and added the statement of the equivariant stable Whitehead theorem, cross-linked with the relevant bits at equivariant homotopy theory, etc. I have also been expanding a little more at RO(G)-grading and cross-linked more with old material at equivariant cohomology. Tried to make the link between RO(G)-grading and equivariant suspension isomorphism more explicit.
Just in case you are watching the logs and are wondering. I am not announcing every single edit, unless there is anything noteworthy.
started some minimum at exceptional field theory (the formulation of 11d supergravity that makes the exceptional U-duality symmetry manifest)
have added a tad more to the Properties-section at Riemann zeta function.
have created a “floating TOC” notions of subcategory and have included it in the relevant entries
Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “E10” from the top and added one for “E10” at the bottom of the page.)
A stub for M-theory. What’s supposed to be so mysterious about it? Is it that people don’t even know what form it would take?
the link to the picture in the entry Charles Wells is broken. Does anyone know how to fix it or have an alternative picture?
Added this pointer:
An early discussion of automata via string diagrams in the Cartesian monoidal category of finite sets:
- Günter Hotz, Eine Algebraisierung des Syntheseproblems von Schaltkreisen, EIK, Bd. 1, (185-205), Bd, 2, (209-231) 1965 (part I, part II, compressed and merged pdf)
incuding that new compressed and merged pdf which I produced, as a service to the community.
In looking for texts that would address the question “What is computation?” and arrive at an answer vaguely akin to path lifting/transport, I found (and have now added pointer to) this text:
which gets pretty close, in particular in and around their Figure 1.
In locally cartesian closed category, I wrote out an explicit proof that pullback functors between slices preserve exponentials (so that Frobenius reciprocity is satisfied).
I added some examples of virtual double categories that do not have composites described in Crutwell-Shulman.
A stub recording a reference:
In a double category with companions, a retrocell is …
In the double category of spans, a retrocell boils down to a morphism of spans, where the source span is the pullback of the original source span along the corresponding horizontal arrow. (Paré, §5.)
Expanded dinatural transformation a little with examples and references.
added pointer to:
Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor
Todo: add more proofs of this result.
For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:
An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out
How can I fix this?
