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2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions 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-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 infinity integration integration-theory k-theory lie lie-theory limit 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 multicategories nonassociative noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string-theory subobject 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 topicSTU relation
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 30th 2019

- Discussion Type
- discussion topic4-sphere
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 30th 2019

added this to the list of references:

Speculative remarks on the possible role of maps from spacetime to the 4-sphere in some kind of quantum gravity via spectral geometry are in

- Ali Chamseddine, Alain Connes, Viatcheslav Mukhanov, section 4 of
*Geometry and the Quantum: Basics*, JHEP 12 (2014) 098 (arXiv:1411.0977)

reviewed in

Alain Connes, section 4 of

*Geometry and the Quantum*, Foundations of Mathematics and Physics One Century After Hilbert. Springer, Cham, 2018. 159-196 (arXiv:1703.02470)Alain Connes, from 58:00 to 1:25:00 in

*Why Four Dimensions and the Standard Model Coupled to Gravity - A Tentative Explanation From the New Geometric Paradigm of NCG*, talk at IHES, 2017 (video recording)

- Ali Chamseddine, Alain Connes, Viatcheslav Mukhanov, section 4 of

- Discussion Type
- discussion topicalgebraic topology
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Mike Shulman
- Last Active Nov 30th 2019

I have tried to give

*algebraic topology*a better Idea-section.

- Discussion Type
- discussion topiccategory with class structure
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 6
- Last comment by Mike Shulman
- Last Active Nov 30th 2019

- Discussion Type
- discussion topicexponential object
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Mike Shulman
- Last Active Nov 29th 2019

I had started an entry “exponentiation” but then thought better of it and instead expanded the existing exponential object: added an examples-section specifically for $Set$ and made some remarks on exponentiation of numbers.

- Discussion Type
- discussion topicAndré Joyal
- Category Latest Changes
- Started by Tim_Porter
- Comments 5
- Last comment by Tim_Porter
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicJackiw-Teitelboim gravity
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicbase change
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicarrow category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicJussi Kalkkinen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicD6-D8-brane bound state
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicchord diagrams modulo 4T are Jacobi diagrams modulo STU
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 29th 2019

starting something, recording Theorem 6 in

- Dror Bar-Natan,
*On the Vassiliev knot invariants*, Topology Volume 34, Issue 2, April 1995, Pages 423-472 (doi:10.1016/0040-9383(95)93237-2, pdf)

not done yet…

- Dror Bar-Natan,

- Discussion Type
- discussion topicJacobi diagram
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 29th 2019

- Discussion Type
- discussion topicchord diagram
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 7
- Last comment by Urs
- Last Active Nov 29th 2019

I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.

- Discussion Type
- discussion topictraced monoidal category
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Mike Shulman
- Last Active Nov 28th 2019

created

*traced monoidal category*with a bare minimumI would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.

- Discussion Type
- discussion topicstar-autonomous category
- Category Latest Changes
- Started by Mike Shulman
- Comments 21
- Last comment by Mike Shulman
- Last Active Nov 28th 2019

I added to star-autonomous category a mention of “$\ast$-autonomous functors”.

- Discussion Type
- discussion topicGeoffrey Penington
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 28th 2019

brief

`category:people`

-entry for hyperlinking references at*black hole information paradox*,*holographic entanglement entropy*and elsewhere

- Discussion Type
- discussion topicZhenbin Yang
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 28th 2019

brief

`category:people`

-entry for hyperlinking references at*black hole information paradox*,*holographic entanglement entropy*and elsewhere

- Discussion Type
- discussion topicBekenstein-Hawking entropy
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 28th 2019

added pointer, here and in related entries, to

- Gary Gibbons, Malcolm J. Perry,
*Black Holes and Thermal Green Functions*, Vol. 358, No. 1695 (1978) (jstor:79482)

being one of the early references considering the computation of black hole radiation in terms of thermal field theory on Wick-rotated spacetimes with compact/periodic “Euclidean time”.

- Gary Gibbons, Malcolm J. Perry,

- Discussion Type
- discussion topicIsbell duality
- Category Latest Changes
- Started by spitters
- Comments 26
- Last comment by David_Corfield
- Last Active Nov 28th 2019

http://ncatlab.org/nlab/show/Isbell+duality

Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here. http://mathoverflow.net/questions/84641/theme-of-isbell-duality

However, this paper http://www.emis.ams.org/journals/TAC/volumes/20/15/20-15.pdf

seems to use another definition. Could someone please clarify?

- Discussion Type
- discussion topicbrane
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Nov 28th 2019

expanded brane

first a little remark on what D-branes are abstractly, in reply to an MO-question, then something on fundamental branes, going along with the discussion on the Café

- Discussion Type
- discussion topictrace of horizontal to round chord diagrams
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 28th 2019

- Discussion Type
- discussion topic4T relation
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 28th 2019

- Discussion Type
- discussion topicWhitehead theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Nov 27th 2019

created Whitehead theorem, including its (oo,1)-topos version

in that context I also created hypercomplete (infinity,1)-topos. maybe that should be merged eventually with hypercompletion.

- Discussion Type
- discussion topicspecial linear Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 27th 2019

- Discussion Type
- discussion topicD-module
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Nov 27th 2019

I tried to implement the connection between D-modules and quasicoherent sheaves a bit more

added to D-module the alternative definition in terms of quasicoherent sheaves of the deRham space

added to deRham space accordingly a pointer to D-modules (also fixed wrong notation in the formulas there)

added to quasicoherent sheaf at the very bottom a pointer to D-modules.

This needs improving. Notably good references should be given.

- Discussion Type
- discussion topicD3-D5 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 27th 2019

for completeness and for recording

- Davide Gaiotto, Edward Witten,
*Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory*, J Stat Phys (2009) 135: 789 (arXiv:0804.2902)

and the fuzzy funnel-geometry reviewed/highlighted in

- {#Fazzi17} Marco Fazzi, Section 3.2.3 of:
*Higher-dimensional field theories from type II supergravity*(arxiv:1712.04447)

- Davide Gaiotto, Edward Witten,

- Discussion Type
- discussion topicKoszul duality
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Nov 27th 2019

Added

- Jonathan Beardsley, Maximilien Péroux,
*Koszul Duality in Higher Topoi*, (arXiv:1909.11724)

- Jonathan Beardsley, Maximilien Péroux,

- Discussion Type
- discussion topicweight systems are associated graded of Vassiliev invariants
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 27th 2019

starting something, in order to record Theorem 1 in

- Dror Bar-Natan,
*On the Vassiliev knot invariants*, Topology Volume 34, Issue 2, April 1995, Pages 423-472 (doi:10.1016/0040-9383(95)93237-2, pdf)

- Dror Bar-Natan,

- Discussion Type
- discussion topicLev Rozansky
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 27th 2019

brief

`category:people`

-entry for hyperlinking references at*Rozansky-Witten theory*