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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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry computable-mathematics computer-science connection constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry 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 limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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 stack 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 topicHopf-Wess-Zumino term
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicAnthony Zee
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicPin(2)
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active 4 days ago

- Discussion Type
- discussion topichigher gauge theory
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by DavidRoberts
- Last Active 5 days ago

I have spent some minutes starting to put some actual expository content into the Idea-section on

*higher gauge theory*. Needs to be much expanded, still, but that’s it for the moment.

- Discussion Type
- discussion topicDold-Thom theorem
- Category Latest Changes
- Started by David_Corfield
- Comments 31
- Last comment by Tim Campion
- Last Active 5 days ago

Added (not very elegantly) the relation to Meyer-Vietoris sequence at Dold-Thom theorem.

- Discussion Type
- discussion topicpremonoidal category
- Category Latest Changes
- Started by Mike Shulman
- Comments 26
- Last comment by Sam Staton
- Last Active 5 days ago

Somebody named Adam left a comment box a while ago at premonoidal category saying that naturality of the associator requires three naturality squares. I believe that this is true when phrased explicitly in terms of one-variable functors, but the slick approach using the “funny tensor product” allows us to rephrase it as a single natural transformation between functors $C\otimes C\otimes C\to C$. I’ve edited the page accordingly. I also added the motivating example (the Kleisli category of a strong monad) and a link to sesquicategory.

There is a comment on the page that “It may be possible to weaken the above make $(Cat,\otimes)$ a symmetric monoidal 2-category, in which a monoid object is precisely a premonoidal category”. However, the Power-Robinson paper says that “We remark that $(C \otimes -) : Cat \to Cat$ is not a 2-functor,” which seems to throw some cold water on the obvious approach to that idea. Was the thought to define a different 2-categorical structure on $Cat$ than the usual one, e.g. using unnatural transformations? It seems that at least one would still have to explicitly require centrality of the coherence isomorphisms.

- Discussion Type
- discussion topicquark
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicWhitehead integral formula
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

am finally splitting this off from

*Hopf invariant*

- Discussion Type
- discussion topicWess-Zumino-Witten model
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

added inspire and doi identifiers for

- Edward Witten,
*Global aspects of current algebra*, Nucl. Phys. B223, 422 (1983) (spire:13234, doi:10.1016/0550-3213(83)90063-9)

- Edward Witten,

- Discussion Type
- discussion topicThom-Gysin sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

added doi for

- Robert Switzer,
*Algebraic Topology - Homotopy and Homology*, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Vol. 212, Springer-Verlag, New York, N. Y., 1975 (doi:10.1007/978-3-642-61923-6)

- Robert Switzer,

- Discussion Type
- discussion topicHopf invariant
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active 6 days ago

I have been making trivial edits (adding references, basic statements, cross-links ) to

*Hopf invariant*and a bunch of related entries, such as*Kervaire invariant*,*Hopf invariant one problem*,*Arf-Kervaire invariant problem*,*normed division algebra*.

- Discussion Type
- discussion topicprototype CLF
- Category Latest Changes
- Started by atmacen
- Comments 43
- Last comment by atmacen
- Last Active 6 days ago

- Discussion Type
- discussion topickernel of integration is the exact differential forms
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by David_Corfield
- Last Active 6 days ago

created an entry for the statement that the

*kernel of integration is the exact differential forms*with a pointer to a proof, and cross-linked with*Lie integration*and*de Rham theorem*

- Discussion Type
- discussion topicMarkus Fröb
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

brief

`category:people`

-entry for hyperlinking references at*L-infinity algebra*and*perturbative quantum field theory*

- Discussion Type
- discussion topicL-infinity algebras in physics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 6 days ago

added pointer to these two recent references, identifying further $L_\infty$-algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:

Markus B. Fröb,

*Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories*(arXiv:1803.10235)Alex Arvanitakis,

*The $L_\infty$-algebra of the S-matrix*(arXiv:1903.05643)

- Discussion Type
- discussion topicrepresentable morphism
- Category Latest Changes
- Started by zskoda
- Comments 10
- Last comment by Mike Shulman
- Last Active 7 days ago

New entry representable morphism, in the sense of Grothendieck school. The notion is used at closed immersion of schemes where I just made some changes.

- Discussion Type
- discussion topicpyknotic set
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 13
- Last comment by Mike Shulman
- Last Active 7 days ago

- Discussion Type
- discussion topicM5-brane
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active 7 days ago

I have added to

*M5-brane*a fairly detailed discussion of the issue with the fractional quadratic form on differential cohomology for the dual 7d-Chern-Simons theory action (from Witten (1996) with help of Hopkins-Singer (2005)).In the new section

*Conformal blocks and 7d Chern-Simons dual*.

- Discussion Type
- discussion topicStefan Förste
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

brief

`category:people`

-entry for hyperlinking references at*gauged WZW model*

- Discussion Type
- discussion topicgauged WZW model
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 7 days ago

started

*gauged WZW model*, but no content yet, am just recording some references…

- Discussion Type
- discussion topicSachdev-Ye-Kitaev model
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicinfrared divergence
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 7 days ago

added pointer to yesterday’s

- Paweł Duch,
*Infrared problem in perturbative quantum field theory*(arXiv:1906.00940)

- Paweł Duch,

- Discussion Type
- discussion topicPeter Haine
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicprofinite homotopy type
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Jun 10th 2019

- Discussion Type
- discussion topiccategorical algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jun 10th 2019

Edited the text in the Idea-section, such as to make the terms

*monoidal category*,*monoid objects*,*module objects*appear.

- Discussion Type
- discussion topicabsolute pushout
- Category Latest Changes
- Started by Emily Riehl
- Comments 3
- Last comment by Mike Shulman
- Last Active Jun 10th 2019

- Discussion Type
- discussion topicuniversal coefficient theorem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Jun 10th 2019

started universal coefficient theorem

- Discussion Type
- discussion topicdensity
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Dmitri Pavlov
- Last Active Jun 10th 2019

I noticed that we had no entry

*density*, so I very briefly created one. While cross-linking it, I noticed that at*volume form*there is related discussion re “pseudo-volume forms”. Maybe somebody here would enjoy to add a bit more glue? (I won’t at the moment.)

- Discussion Type
- discussion topicn-localic (infinity,1)-topos
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jun 9th 2019

Has anyone written down an analogue for $(\infty,1)$-toposes of the (hyperconnected, localic) factorization system for 1-toposes? In particular, is it known that $n$-localic $(\infty,1)$-toposes form a reflective subcategory of all $(\infty,1)$-toposes?

- Discussion Type
- discussion topicfunctional cup product
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 9th 2019