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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
stub for quantum computation
added at adjoint functor
more details in the section In terms of universal arrows;
a bit in the section Examples
Added to Dedekind cut a short remark on the ¬¬-stability of membership in the lower resp. the upper set of a Dedekind cut.
I have added some accompanying text to the list of links at monad (disambiguation).
One question: in the entry Gottfried Leibniz it is claimed that the term “monad” for a functor on a category with monoid structure also follows Leibniz’s notion of monads. Is this really so? What’s a reference for this claim?
I am asking because I don’t see how the notion of monoid in the endomorphisms of a category would be related to what Leibniz was talking about. What’s the idea, if there is one?
added reference to derived category
added pointer to:
Julian Schwinger: Quantum Kinematics and Dynamics, CRC Press (1969, 1991) [ISBN:9780738203034, pdf]
Julian Schwinger (ed.: Berthold-Georg Englert): Quantum Mechanics – Symbolism of Atomic Measurements, Springer (2001) [doi:10.1007/978-3-662-04589-3]
with a link to arguments that Schwinger secretly (re-)invented groupoid algebra, in these books.
a stub entry, for the moment just to make a link work that has long been requested at Handbook of Quantum Gravity
for the equivariant+twisted version I added further pointer to
El-kaïoum M. Moutuou, Graded Brauer groups of a groupoid with involution, J. Funct. Anal. 266 (2014), no.5 (arXiv:1202.2057)
Daniel Freed, Gregory Moore, Section 7 of: Twisted equivariant matter, Ann. Henri Poincaré (2013) 14: 1927 (arXiv:1208.5055)
Kiyonori Gomi, Freed-Moore K-theory (arXiv:1705.09134, spire:1601772)
just the other day I was searching for good references on “asymptotic symmetries”, not finding much. But today appears the useful
and so I am starting an entry hereby
a bare list of references, to be !include-ed into the References-sections of relevant entries (such as knot homology, topological string theory) for ease of synchronization
added at Grothendieck universe at References a pointer to the proof that these are sets of κ-small sets for inaccessible κ. (also at inaccessible cardinal)
Together with my PhD students, I have been thinking a lot recently about the appropriate notion of a module over a C^∞-ring, i.e., something with better properties than Beck modules, which boil down to modules over the underlying real algebra in this case.
We stumbled upon the article C-infinity module (schreiber).
It says: “a C-infty algebra A is a copresheaf A∈Quantities=CoPrSh(CartesianSpaces) which becomes a copresheaf with values in algebras when restricted along FinSet↪CartesianSpaces,”
Why are we restricting to FinSet here? The underlying commutative real algebra is extracted by restricting to the Lawvere theory of commutative real algebras, i.e., CartesianSpaces_Poly, the subcategory of cartesian spaces and polynomial maps. Restricting to FinSet^op (as opposed to FinSet) extracts the underlying set only. It is unclear what is being meant by restricting along FinSet→CartesianSpaces, since the latter functor does not preserve finite products, so restricting along it does not produce a functor between categories of algebras over Lawvere theories.
In this entry, generating functional redirects to generating function. This use does not seem to match the context.
added some formatting and some cross-links (nilpotent groups!) and added pointer to:
stub at locally compact locale
Added:
Introducing hyperstonean spaces:
Added to T-duality a section with the discussion of the usual path-integral heuristics for why the two sigma-models on T-dual backgrounds yield equivalent quantum field theories.
am in the process of adding some notes on how the D=5 super Yang-Mills theory on the worldvolume of the D4-brane is the double dimensional reduction of the 6d (2,0)-superconformal QFT in the M5-brane.
started a stubby double dimensional reduction in this context and added some first further pointers and references to M5-brane, to D=5 super Yang-Mills theory and maybe elsewhere.
But this still needs more details to be satisfactory, clearly.
Just noticed that we have a duplicate page Jon Sterling.
I have now moved the (little but relevant) content (including redirects) from there to here.
Unfortunately, the page rename mechanism seems to be broken until further notice, therefore I am hesitant to clear the page Jon Sterling completely, for the time being.
I looked at real number and thought I could maybe try to improve the way the Idea section flows. Now it reads as follows:
A real number is something that may be approximated by rational numbers. Equipped with the operations of addition and multiplication induced from the rational numbers, real numbers form a number field, denoted ℝ. The underlying set is the completion of the ordered field ℚ of rational numbers: the result of adjoining to ℚ suprema for every bounded subset with respect to the natural ordering of rational numbers.
The set of real numbers also carries naturally the structure of a topological space and as such ℝ is called the real line also known as the continuum. Equipped with both the topology and the field structure, ℝ is a topological field and as such is the uniform completion of ℚ equipped with the absolute value metric.
Together with its cartesian products – the Cartesian spaces ℝn for natural numbers n∈ℕ – the real line ℝ is a standard formalization of the idea of continuous space. The more general concept of (smooth) manifold is modeled on these Cartesian spaces. These, in turnm are standard models for the notion of space in particular in physics (see spacetime), or at least in classical physics. See at geometry of physics for more on this.
category: people page for the reference
Anonymouse
Stub Frobenius reciprocity.
stub for confinement, but nothing much there yet. Just wanted to record the last references there somewhere.
I added the reference