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brief category:people entry for hyperlinking references at geometric fixed point spectrum
slightly expanded the Idea-section,
added pointer to the lecture notes by Andrew Blumberg,
cross-linked with Mackey-functor and enriched (∞,1)-functor
stub entry, for the moment just for the purpose of facilitating cross-links from/to Mackey functor
discovered this ancient entry (while searching for occurences of “permutation matrix” on the nLab). This was in very bad shape, with a ill-rendering floating toc and big query box right at the beginning, then a little bit of content, and then some speculation by a contributor who we had to persuade to leave, long ago.
I did a minimum of cleaning up, in particular removed the query box, since it had been dealt with. This is what it had said:
+– {.query}
Zoran: there are several things called “Birkhoff’s theorem” in various field of mathematics and mathematical physics, and belong even to at least 2 different classical Birkhoff’s. Even wikipedia has pages for more than one such theorem. To me the first which comes to mind is Birkhoff’s factorization theorem, now also popular in Kreimer-Connes-Marcolli work and in connection to loop groups (cf. book by Segal nad Pressley). I would like that the nlab does not mislead by distinguishing one of the several famous Bikhoff labels without mentioning and directing to 2-3 others.
Ian Durham: Good point. I think this probably ought to be renamed the “Birkhoff-von Neumann theorem.” Is that a good enough label or should we get more specific with it?
Toby: I have moved it. See also the new page Birkhoff’s theorem, which is basically just Zoran's comment above. =–
brief category:people-entry for hyperlinking references at de Sitter spacetime
brief category:people-entry for hyperlinking references at Bayesian interpretation of quantum mechanics
brief category:people-entry for the purpose of hyperlinking references at Feit-Thompson theorem and at permutation representation
Few words added at Catalan number.
stub entry, for the moment just so as to record the reference: the analog of Atiyah-Segal completion, but now for algebraic K-theory over a finite field.
brief category:people-entry for hyperlinking refernces at Kahn-Priddy theorem and stable cohomotopy
brief category:people-entry for hyperlinking references at K-theory of a permutative category and field with one element and algebraic K-theory
made this entry cross-link with Segal-Carlsson theorem, added pointer to the proof in
added the crucial pointer to
and a bit more
brief category:people-entry in for the purpose of hyperlinking references at discrete torsion, ABJM theory and supergravity C-field
I have slightly expanded, reorganized and polished the entry state. (Added definition of classical state in Heisenberg picture, added pointer to the entry classical state, moved pointers to quasi-state and state in AQFT and operator algebra to the paragraph on quantum states and added at the very end a list of “related concepts” in an attempt to organize what used to be somewhat of a mess here). But this entry deserves to be polished and organized and expanded still more.
created a stub entry topological recursion in order to record some references, and added cross-links with various related entries
Added a reference to plane graph. (Started this thread since it appear not to have had one.)
We don’t have anything on this, I think, but there is mention of “intrinsic” and “à la Church” at coercion. From Type refinement and monoidal closed bifibrations:
One of the difficulties in giving a clear mathematical definition of the “topic” of type theory is that the word “type” is actually used with two very different intuitive meanings and technical purposes in mind:
- Like the syntactician’s parts of speech, as a way of defining the grammar of well-formed expressions.
- Like the semanticist’s predicates, as a way of identifying subsets of expressions with certain desirable properties.
These two different views of types are often associated respectively with Alonzo Church and Haskell Curry (hence “types à la Church” and “types à la Curry”), while the late John Reynolds referred to these as the intrinsic and the extrinsic interpretations of types [11]. In the intrinsic view, all expressions carry a type, and there is no need (or even sense) to consider the meaning of “untyped” expressions; while in the extrinsic view, every expression carries an independent meaning, and typing judgments serve to assert some property of that meaning.
[11] is John C. Reynolds. The Meaning of Types: from Intrinsic to Extrinsic Semantics. BRICS Report RS-00-32, Aarhus University, December 2000. pdf
There are two very different ways of giving denotational semantics to a programming language (or other formal language) with a nontrivial type system. In an intrinsic semantics, only phrases that satisfy typing judgements have meanings. Indeed, meanings are assigned to the typing judgements, rather than to the phrases themselves, so that a phrase that satisfies several judgements will have several meanings.
In contrast, in an extrinsic semantics, the meaning of each phrase is the same as it would be in a untyped language, regardless of its typing properties. In this view, a typing judgement is an assertion that the meaning of a phrase possesses some property.
The terms “intrinsic” and “extrinsic” are recent coinages by the author [1, Chapter 15], but the concepts are much older. The intrinsic view is associated with Alonzo Church, and has been called “ontological” by Leivant [2]. The extrinsic view is associated with Haskell Curry, and has been called “semantical” by Leivant.
[1] John C. Reynolds. Theories of Programming Languages. Cambridge University Press, Cambridge, England, 1998. [2] Daniel Leivant. Typing and computational properties of lambda expressions. Theoretical Computer Science, 44(1):51–68, 1986.
Anyone have a preferred name for this distinction?
created simplicial homology (instead of cellular homology)
minimum category:people-entry for the purpose of hyperlinking references at Berry phase and at asymptotic series
am starting some minimum at membrane instanton
I edited subobject slightly and added the statement that in an accessible category C every poset of subobjects is small.
Removed by admin.
Began working on a write up of the material presented in #1 at this nForum post. I will use it as well to experiment with introduction of further Tex style commands (the aim is for the page to compile as-is into LaTex), and to work on relevant nLab pages on knot theory (beginning with link diagram earlier today).
added pointer to a reference: Borceux 94, Vol 1, section 4.4
Tried to make some improvements. Added a redirect for Reidemeister’s theorem. Gave a hint of how to prove it. Quite a bit more could be done to improve the page.
