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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.
polished and expanded adjoint (infinity,1)-functor
the entry modular tensor category was lacking (among many things that it is still lacking) some pointers to literature that reviews the relation to QFT. I have added a handful, maybe the best one is this here:
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.
in analogy to what I just did at classical mechanics, I have now added some basic but central content to quantum mechanics:
Quantum mechanical systems
States and observables
Spaces of states
Flows and time evolution
Still incomplete and rough. But I have to quit now.
created a currently fairly empty entry quantum measurement, just so as to have a place where to give a commented pointer to the article
In the category:people-entry “William Lawvere” I have created a subsection “Motivation from foundations of physics” where I want to collect pointers to where and how Lawvere was/is motivated from finding foundations for (classical continuum) physics.
Explicit evidence for this that I am aware of includes notably the texts Toposes of laws of motion and the introduction to the book Categories in Continuum Physics.
The Wikipedia entry has this about motivation from physics:
Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. meeting on “Categories in Continuum Physics” in 1982. Clifford Truesdell participated in that meeting, as did several other researchers in the rational foundations of continuum physics and in the synthetic differential geometry which had evolved from the spatial part of Lawvere’s categorical dynamics program). Lawvere continues to work on his 50-year quest for a rigorous flexible base for physical ideas, free of unnecessary analytic complications.
Question: Can anyone point me to more on this early phase of the story (graduate student is supposed to start to look into continuum mechanics, starts to wonder “What is a vector field, really?, what a differential equation?” and ends up revolutionizing the foundations of differential calculus)?
created over-topos
just to make links work, I have started a minimum at gravitational wave.
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
We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.
added pointer to today’s
created stub for 6d (2,0)-supersymmetric QFT, mainly to record the references for the moment
added to the Idea-section (here) the description of PT-collapse as the function that assigns “asymptotic distance form the submanifold”, an illustrating graphics, and a comment that this represents the Cohomotopy charge of the submanifold