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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I wanted to be able to use the link without it appearing in grey, so I created a stub for general relativity.
I added to star-autonomous category a mention of “-autonomous functors”.
Added
the first now of ’Selected writings’.
now creating this entry.
The technical material under “Details” (here) is copied over from what I had written at reader monad – Examples – quantum reader monad. (There may still be room left to adjust the wording in order to reflect that this material moved to a new entry.)
To this I have now added an Idea-section (here) which highlights the relation to (equivalence with) Bob Coecke’s “classical structures” (which term I made redirect to here now)
In order to accompany the nCafe discussion I have started to add some content to the entry Euler characteristic
brief category:people-entry for hyperlinking references at quantum spin Hall effect
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
created an entry modal type theory; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with monad (in computer science).
a bare list of references, to be !include-ed into the References-section of relevant entries (such as at braid group representation and at semi-metal).
Had originally compiled this list already last April (for this MO reply) but back then the nLab couldnt be edited
added (here) pointer to Russell’s 1922 speech Free Thought and Official Propaganda, with some quotes
recorded some recent surveys of the status of MOND at MOND
Added selected writings section and reference
In the examples section of extensive category, it is stated that the category of affine schemes is infinitary extensive.
For all I know, I was the one who stuck in that example. But is that statement actually true? I’m having trouble seeing it.
If is a commutative ring over (by which I mean under (-:), does the functor preserve arbitrary cartesian products? Because it seems that’s what we basically need for the statement to be true.
I created a stub certified programming.
That’s motivated from me having expanded the Idea-section at type theory. I enjoyed writing the words “is used in industry”. There are not many Lab pages where I can write these words.
I am saying this only half-jokingly. Somehow there is something deep going on.
Anyway, in (the maybe unlikely) case that somebody reading this here has lots of information about the use and relevance of certified programming in industry, I’d enjoy seeing more information added to that entry.
I have expanded out the statement of (the ingredients of) the isomorphism a bit more and made explicit the statement of the relation to the Landweber exact functor theorem.
added pointer to
Victor Snaith, Algebraic Cobordism and K-theory, Mem. Amer. Math. Soc. no 221 (1979)
Victor Snaith, Towards algebraic cobordism, Bull. Amer. Math. Soc. 83 (1977), 384-385 (doi:10.1090/S0002-9904-1977-14281-X)
Also tried to fix the ordering of the rest of the reference, but I give up for the moment. This needs attention by some expert
Created W-type.
created directed homotopy type theory
I am moving the following old query box exchange from orbifold to here.
old query box discussion:
I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely does not view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.
Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?
Urs Schreiber: please, go ahead. It would be appreciated.
end of old query box discussion
I removed some spam on category theory.
a brief category:disambigation-page, for the moment just to ensure that the reader of 2-type theory will find an unbroken link for directed type theory which will alert them of the existence of directed homotopy type theory
I am finally creating this entry — meant as a bare list of hyperlinked terms to be !include-ed into the “Related concepts”-sections of the respective entries — for ease of synchronizing this list across all these entries.
(I am not sold on the title “mathematical statements”, it’s just the best I could come up with after a minute of thinking about it).
I am creating this now with the following list, but this may change as I now go through all the related entries:
Added an Idea-section to this (previously stubby) entry — not meant to be definite, just what came to mind when finding that such a section was still lacking here:
In mathematics, a conjecture is a proposition which is expected to be true, hence expected to have a proof, but for which no proof is (currently) known.
Hence being a conjecture is a sociological aspect of a proposition, not a mathematical aspect: Once a proof (or else a counterexample) is found, the conjecture ceases to be a conjecture and instead becomes a theorem.
It happens that conjectures remain unproven while being perceived as trustworthy enough that further theorems are proven assuming the conjectures – in this case the conjecture plays the role of a hypothesis in the sense of formal logic.
For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).
In other cases the term “hypothesis” is used synonymously with “conjecture” – e.g. for the homotopy hypothesis (key cases of which have long become theorems) or the cobordism hypothesis (on which a proof has famously been claimed but not universally accepted).
cross-linked with conjecture, adding these lines (following after the paragraph that starts out with “In formal logic…”):
In the practice of mathematics (or beyond), hypotheses that that are expected to have a proof, even if currently unknown, are known as conjectures.
For example, the “standard conjectures” in algebraic geometry serve as hypotheses in a wealth of theorems which are all proven (only) “assuming the standard conjectures” (cf. e.g. arXiv:9804123).
added pointer to:
added a section Spaces of infinitesimal simplices
one possible bit of information at flux
this is a bare section, meant to be !include-ed into relevant entries (such as at superconductor, vortex, Dirac charge quantization and maybe elsewhere) as mentioned here