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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicDomenico Fiorenza
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Feb 2nd 2020

- Discussion Type
- discussion topicinternal hom of algebras over a commutative monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 3
- Last comment by Todd_Trimble
- Last Active Feb 2nd 2020

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.

- Discussion Type
- discussion topicadjoint (infinity,1)-functor
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Feb 2nd 2020

polished and expanded adjoint (infinity,1)-functor

- Discussion Type
- discussion topicstrong monad
- Category Latest Changes
- Started by Sam Staton
- Comments 13
- Last comment by PaoloPerrone
- Last Active Feb 1st 2020

- Discussion Type
- discussion topiccommutative monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 5
- Last comment by PaoloPerrone
- Last Active Feb 1st 2020

- Discussion Type
- discussion topicmodular tensor category
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Joe Moeller
- Last Active Feb 1st 2020

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:- Eric Rowell,
*From quantum groups to Unitary modular tensor categories*, Contemporary Mathematics 2005 (arXiv:math/0503226)

- Eric Rowell,

- Discussion Type
- discussion topicM2-M5 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 1st 2020

- Discussion Type
- discussion topicDp-D(p+2)-brane intersections in fuzzy funnels -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 1st 2020

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.

- Discussion Type
- discussion topicDp-D(p+2)-brane bound state
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Feb 1st 2020

- Discussion Type
- discussion topicgraded monad
- Category Latest Changes
- Started by David_Corfield
- Comments 20
- Last comment by David_Corfield
- Last Active Feb 1st 2020

- Discussion Type
- discussion topicsu(2)
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Feb 1st 2020

- Discussion Type
- discussion topicquantum mechanics
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Feb 1st 2020

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.

- Discussion Type
- discussion topicquantum measurement
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Feb 1st 2020

created a currently fairly empty entry

*quantum measurement*, just so as to have a place where to give a commented pointer to the article- Klaas Landsman, Robin Reuvers,
*A Flea on Schrödinger’s Cat*, Found. Phys. 43, 373-407 (2013) (arXiv:1210.2353)

- Klaas Landsman, Robin Reuvers,

- Discussion Type
- discussion topicWilliam Lawvere
- Category Latest Changes
- Started by Urs
- Comments 40
- Last comment by David_Corfield
- Last Active Jan 31st 2020

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)?

- Discussion Type
- discussion topicpiecewise flat spacetime
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jan 31st 2020

- Discussion Type
- discussion topicover-topos
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Jan 30th 2020

created over-topos

- Discussion Type
- discussion topicaction monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 8
- Last comment by PaoloPerrone
- Last Active Jan 30th 2020

- Discussion Type
- discussion topicCauchy theorem
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Jan 30th 2020

- Discussion Type
- discussion topicsoft graviton theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 30th 2020

- Discussion Type
- discussion topicgravitational wave
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Jan 30th 2020

just to make links work, I have started a minimum at

*gravitational wave*.

- Discussion Type
- discussion topicsuper 2-brane in 4d
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 30th 2020

added pointer to discussion of coupling of the super 2-brane in 4d to D=4 N=1 super Yang-Mills theory:

- Igor Bandos, Stefano Lanza, Dmitri Sorokin,
*Supermembranes and domain walls in $\mathcal{N}=1$, $D=4$ SYM*(arXiv:1905.02743)

- Igor Bandos, Stefano Lanza, Dmitri Sorokin,

- Discussion Type
- discussion topicoptic (in computer science)
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by David_Corfield
- Last Active Jan 30th 2020

- Discussion Type
- discussion topicgeometric Langlands correspondence
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Jan 30th 2020

a beginning at geometric Langlands correspondence

- Discussion Type
- discussion topiclarge N limit
- Category Latest Changes
- Started by zskoda
- Comments 12
- Last comment by Urs
- Last Active Jan 29th 2020

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.

- Discussion Type
- discussion topicAlexander polynomial
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 29th 2020

added pointer to today’s

- V. Mishnyakov, A. Sleptsov, N. Tselousov,
*A new symmetry of the colored Alexander polynomial*(arXiv:2001.10596)

- V. Mishnyakov, A. Sleptsov, N. Tselousov,

- Discussion Type
- discussion topicstructure formation
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Jan 29th 2020

- Discussion Type
- discussion topicfunctoriality of categories of presheaves
- Category Latest Changes
- Started by anuyts
- Comments 2
- Last comment by David_Corfield
- Last Active Jan 29th 2020

- Discussion Type
- discussion topicD=6 N=(2,0) SCFT
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Jan 29th 2020

created stub for 6d (2,0)-supersymmetric QFT, mainly to record the references for the moment

- Discussion Type
- discussion topicChern-Simons Wilson lines in AdS3-CFT2 -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 28th 2020

- Discussion Type
- discussion topicPontrjagin-Thom collapse map
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 28th 2020

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