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stub for quantum computation
crated D'Auria-Fre formulation of supergravity
there is a blog entry to go with this here
Adding reference
Anonymous
merging some information from the articles on equality and natural deduction into its own article about conversion rules.
Anonymous
added publication data to:
there had been no references at Hilbert space, I have added the following, focusing on the origin and application in quantum mechanics:
John von Neumann, Mathematische Grundlagen der Quantenmechanik. (German) Mathematical Foundations of Quantum Mechanics. Berlin, Germany: Springer Verlag, 1932.
George Mackey, The Mathematical Foundations of Quamtum Mechanics A Lecture-note Volume, ser. The mathematical physics monograph series. Princeton university, 1963
E. Prugovecki, Quantum mechanics in Hilbert Space. Academic Press, 1971.
I was involved in some discussion about where the word “intensional” as in “intensional equality” comes from and how it really differs from “intenTional” and what the point is of having such a trap of terms.
Somebody dug out Martin-Löf’s lecture notes “Intuitionistic type theory” from 1980 to check. Having it in front of me and so before I forget, I have now briefly made a note on some aspects at equality in the section Different kinds of equalits (below the first paragraph which was there before I arrived.)
Anyway, on p. 31 Martin-Löf has
intensional (sameness of meaning)
I have to say that the difference between “sameness of meaning” and “sameness of intenTion”, if that really is the difference one wants to make, is at best subtle.
started a bare minimum at state monad
added pointer to the original article:
I created the article properad, essentially a brief description of the definition together with a reference.
The entry Lie algebra extension used to have only a discussion of the fairly exotic topic of classification in nonabelian Lie algebra cohomology. I have now added an Idea-section with some more introductory and more traditional remarks. This could well be expanded much further.
the entry that used to be titled quantum mechanics in terms of dagger-compact categories I have renamed into finite quantum mechanics in terms of dagger-compact categories (with a “finite” up front) and I have added to the first sentence the qualifier “finite” and “finite-dimensional” a bunch of times.
I am currently at “Quantum Physics and Logic 2012” in Brussels, and every second speaker advertizes the formalism of what they call “categorical quantum theory”. It’s all fine for the majority of the audience which is all into quantum information theory, where one is only interested in shuffling a finite bunch of qbits around, but it is rather misleading from an ordinary perspective on quantum physics. Already the particle on the line is not a finite quantum system.
Created ε-number.
have split off tensor product of abelian groups from tensor product and expanded slightly
splitting off and expanding this list of references from quantum information theory via dagger-compact categories, to be re-!included there and elsewhere, for ease of syncing
The page split coequalizer said that the canonical presentation of an Eilenberg–Moore algebra is a split coequalizer in the category of algebras. I don’t think that’s right – if I recall correctly it’s reflexive there, but in general not split until you forget down to the underlying category. So I changed the page.
created computational trinitarianism, combining a pointer to an exposition by Bob Harper (thanks to David Corfield) with my table logic/category-theory/type-theory.
A dedicated discussion of the comparison maps between any adjunction and its initial Kleisli- and terminal monadic adjunction is being alluded to in various related entries, but none of them has really been admitting to details or giving any concrete citations.
This entry is meant to fill that gap. It’s unfortunate that this important concept does not have a more descriptive name. I have added some words of disambiguation in order to account for this.
The link for ’equivalent’ at the top redirected to natural isomorphism which (as I understand it) is the correct 1-categorical version of an equivalence of functors, but this initially lead me to believe that a functor was monadic iff it was naturally isomorphic to a forgetful functor from the Eilenberg-Moore category of a monad on its codomain, which would mean that the domain of the functor was literally the Eilenberg-Moore category of some adjunction since natural isomorphism is only defined for parallel functors.
A number of examples and counterexamples have been firmed up at presentation axiom. Some of them devolve on an observation made by Jonas Frey a few days ago at internally projective object, for which I added a simple proof. There are still some points that needed to be clarified regarding the internalization of the presentation axiom, but for now the discussion is concentrated on relations between externally projeective and internally projective objects.
Created extension system.
added publication details for:
added to Stiefel-Whitney class briefly the definition/characterization.
There seems to have remained a typo in the definition (here) of the strong/fine/final topology (probably induced from copy-and-pasting the previous definition of the weak/coarse/initial topology and not adjusting appropriately at all instances): It had the intersection instead of the union of all candidate topologies. I have fixed it (I believe) and have created separate subsections for the two notions.
Preprint today by Yau et al., relating -adic strings to the Riemann zeta function:
I recorded several references at a newly created stub divergent series.
Over at rack, I noticed brief mention of the notion of shelf. As some of you will know, shelves also crop up in large cardinal axioms, so I gave shelf its own subsection and mentioned some of the lore (e.g., Laver tables). The topic might be worth a separate page.