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brief category:people-entry for hyperlinking references at p-adic string theory
brief category:people-entry for hyperlinking references at tensor network state and holographic entanglement entropy
brief category:people-entry for hyperlinking references at tensor network and at holographic entanglement entropy
brief category:people-entry for hyperlinking references at tensor network
brief category:people-entry for hyperlinking references at computational topology
a stub for the moment just so as to give a home to
and to cross-link with p-adic AdS/CFT correspondence and tensor network states.
I edited lambda-ring, added a definition from the thesis of John R. Hopkins. Later on I will add the definitions of Hazewinkel, too. This entry has a long (and very instructive) idea-section. Maybe I find time to fill in some more details to these ideas.
added pointer to today’s
at books about string theory I have added some paragraphs with descriptions of books in the first section (“Mathematically inclined monographs about string theory”)
I see that Ben Webster was so kind to start knot invariant.
That nicely supplies linkes for Bruce's recent Chern-Simons theory
brief category:people-entry for hyperlinking references at cohomotopy
brief category:people-entry for hyperlinking references at AdS/CFT in condensed matter physics
brief category:people-entry for hyperlinking references at AdS/CFT in condensed matter physics
brief category:people-entry for hyperlinking references at quantum probability theory
Can we think of free cocompletion as a left adjoint? In what follows, by ’cocomplete’ I mean ’having all small colimits’.
Free cocompletion can’t be a left adjoint functor from (the category of small categories) to (the category of locally small cocomplete categories), because there’s no right adjoint .
Also surely not from to (the category of small cocomplete categories), because there just aren’t enough small cocomplete categories: only posets.
The article on free cocompletion mentions a free cocompletion functor from (the category of locally small categories) to , studied by Day and Lack. There’s an obvious candidate right adjoint from to . So this might work!
Does it?
Day and Lack work in the enriched case, and I’m a bit confused, but they seem to imply that free cocompletion is a pseudomonad on , which would be a step in the right direction.
Started page, more to come. The content will be more or less dual to the one of tensor product of algebras over a commutative monad, with as little overlap as possible.
This is a bare section to be !include-ed into other relavant entries (notably Dp-D(p+2)-brane intersection and fuzzy funnel, but maybe also elsewhere). It contains one sub-section – and nothing else.
added pointer to discussion of coupling of the super 2-brane in 4d to D=4 N=1 super Yang-Mills theory:
a beginning at geometric Langlands correspondence
added a bit to framed manifold
Detection of the 21cm hydrogen absorption line expected in the CMB has been claimed now. Such a detection is thought to have implications for observational cosmology comparable in relevance to those of the recent gravitational wave detection. I have collected some original articles and reviews here in an otherwise empty entry hydrogen line
I have reorganised set theory and spun off material set theory.
I keep having the need to point to something like mass gap problem. So now I created a stub for it, just so that the links works. Has to be expanded, clearly.
brief category:people-entry for hyperlinking references at flavour problem and flavour anomaly
brief category:people-entry for hyperlinking references at flavour (particle physics) and at flavour anomaly
brief category:people-entry for hyperlinking references at kaon and at flavour anomaly
Todd points out elsewhere that there is a problem with the following sentence in the section Smallness in the context of universes:
is essentially -small if there is a bijection from its set of morphisms to an element of (the same for the set of objects follows); this condition is non-evil.
(introduced in revision 11).
It looks to me that first of all this is not the right condition – the right condition must mention equivalence of categories to a U-small category.
Added the recent
I came to think that the term geometric type theory for the type theory internal toi sheaf toposes should exists. Thanks to Bas Spitter for pointing out that Steve Vickers had already had the same idea (now linked to at the above entry).
Also created geometric homotopy type theory in this vein, with some evident comments.
This is a base topic of my contribution. It introduces a new function that gives series whose coefficients are powers of fine structure constant. Furthermore each member represents natural physical interaction. It can be treated as natural physics that introduces natural particles.
May be I made a lot of mistakes. I will correct them.
created stub for 2-Lawvere theory
added a further quote from
interview with Mike Duff by Graham Fermelo, The universe speaks in numbers – Interview 14 (web):
(7:04) The problem we face is that we have a patchwork understanding of M-theory, like a quilt. We understand this corner and that corner, but what’s lacking is the overarching big picture. So directly or indirectly, my research hopes to explain what M-theory really is. We don’t know what it is.
In a certain sense, and this is not a popular statement, I think it’s premature to be asking: “What are the empirical consequences”, because it’s not yet in a mature enough state, where we can sensibly make falsifiable prediction.