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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 complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 internal-categories itex k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad 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 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 topicCharles Boyer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 21st 2020

brief

`category:people`

-entry for hyperlinking references at*Sasakian geometry*

- Discussion Type
- discussion topicJeff Smith
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 6
- Last comment by Urs
- Last Active Jul 21st 2020

- Discussion Type
- discussion topicMichael Hopkins
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 21st 2020

added some text to the beginning of the category:people entry

*Michael Hopkins*. Currently it reads as follows:Michael Hopkins is a mathematician at Harvard University.

Hopkins is a world leading researcher in algebraic topology and (stable-)homotopy theory.

Among his notable achievements are his work on the Ravenel conjectures, the introduction and discussion of the generalized cohomology theory

*tmf*and its string orientation, a formalization and construction of differential cohomology, the proof of the Kervaire invariant problem. More recently via Jacob Lurie’s work on the cobordism hypothesis Hopkins participates in work related to the foundations of quantum field theory.

- Discussion Type
- discussion topichomotopy coherent diagram
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 21st 2020

I have added to homotopy coherent diagram and to model structure on algebras over an operad the fact that one can describe homotopy coherent diagrams as algebras over the Boardman-Vogt resolution of some operad. Vogt’s rectification theorem is then a special case of the general Berger-Moerdijk result.

In the course of this I reorganized and expanded homtopy coherent diagram a bit. It still needs to be polished a bit.

- Discussion Type
- discussion topicnilpotence theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 21st 2020

brief entry

*nilpotence theorem*(in chromatic homotopy theory, maybe needs disambiguation later…)

- Discussion Type
- discussion topictwisted ordinary differential cohomology
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Urs
- Last Active Jul 21st 2020

- Discussion Type
- discussion topicPhilippe Gaucher
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Jul 21st 2020

- Discussion Type
- discussion topicsemicategory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by nLab edit announcer
- Last Active Jul 21st 2020

I have touched the following entries, trying to interlink them more closely by added sentences with cross-links that indicate how they relate to each other:

Also linked for instance to

*semicategory*from*category*, etc.Linked also to Delta space, but the entry doe not exist yet.

- Discussion Type
- discussion topicequivariant ordinary differential cohomology
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 20th 2020

starting a stub, for the moment just to record references.

There is a plethora of constructions in the literature. Has anyone discussed in detail if/how these relate to the evident general abstract definition (maps of $\infty$-stacks from the given geometric groupoid to the Deligne complex)?

I see that some authors, like Redden, partially go in this direction, but I haven’t seen yet a comprehensive account to this extent.

- Discussion Type
- discussion topicreflective factorization system
- Category Latest Changes
- Started by Mike Shulman
- Comments 7
- Last comment by Urs
- Last Active Jul 20th 2020

Created reflective factorization system.

- Discussion Type
- discussion topicextensive category
- Category Latest Changes
- Started by Sam Staton
- Comments 5
- Last comment by Hurkyl
- Last Active Jul 20th 2020

- Discussion Type
- discussion topicKLT relations
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jul 20th 2020

at

*KLT relations*I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).In this course I also expanded the list of references at quantum gravity – As a perturbative quantum field theory

- Discussion Type
- discussion topicscheme
- Category Latest Changes
- Started by Richard Williamson
- Comments 8
- Last comment by JonasFrey
- Last Active Jul 19th 2020

I found the definition of a scheme to be slightly unclear/insufficiently precise at one point, so I have tweaked things slightly, and added more details. Indeed, it is quite common to find a formulation similar to ’every point has an open neighbourhood isomorphic to an affine scheme’, whereas I think it important to be clear that one does not have the freedom to choose the sheaf of rings on the local neighbourhood, it must be the restriction of the structure sheaf on $X$.

- Discussion Type
- discussion topicorbispace
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 19th 2020

edited at

*orbispace*in order to express Charles Rezk’s statement here more accurately.

- Discussion Type
- discussion topicRita Fioresi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 19th 2020

brief

`category:people`

-entry for hyperlinking references at supergeometry supermanifolds, super Lie groups, functorial geometry

- Discussion Type
- discussion topicClaudio Carmeli
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 19th 2020

brief

`category:people`

-entry for hyperlinking references at supergeometry supermanifolds, super Lie groups, functorial geometry

- Discussion Type
- discussion topicsupermanifold
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jul 19th 2020

I have added a little bit to supermanifold, mainly the definition as manifolds over superpoints, the statement of the equivalence to the locally-ringed-space definition and references.

- Discussion Type
- discussion topicsupergroup
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 19th 2020

Added the Yoneda-embedding way to talk about group objects and hence supergroups.

- Discussion Type
- discussion topiccontact manifold
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Jul 18th 2020

am starting an entry

*contact manifold*

- Discussion Type
- discussion topicCR manifold
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 18th 2020

added pointer to

- Sorin Dragomir, Jun Masamune,
*Cauchy-Riemann orbifolds*, Tsukuba J. Math. Volume 26, Number 2 (2002), 351-386 (euclid:tkbjm/1496164430)

- Sorin Dragomir, Jun Masamune,

- Discussion Type
- discussion topicJanusz Grabowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2020

brief

`category:people`

-entry for hyperlinking references at*embedding of smooth manifolds into formal duals of R-algebras*

- Discussion Type
- discussion topicembedding of smooth manifolds into formal duals of R-algebras
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 18th 2020

I finally gave this statement its own entry, in order to be able to conveniently point to it:

*embedding of smooth manifolds into formal duals of R-algebras*

- Discussion Type
- discussion topicalgebraically compact category
- Category Latest Changes
- Started by Sam Staton
- Comments 7
- Last comment by Sam Staton
- Last Active Jul 18th 2020

- Discussion Type
- discussion topicBordism, Stable Homotopy and Adams Spectral Sequences
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jul 18th 2020

I have been indexing Kochman’s excellent book

*Bordism, Stable Homotopy and Adams Spectral Sequences*and in the course I have touched all the relevant entries

- Discussion Type
- discussion topichypercomplex manifold
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2020

- Discussion Type
- discussion topic(infinity,1)Topos
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 18th 2020

- Discussion Type
- discussion topicG-structure
- Category Latest Changes
- Started by zskoda
- Comments 24
- Last comment by Urs
- Last Active Jul 18th 2020

I do not understand the entry G-structure. G-structure is, as usual, defined there as the principal $G$-subbundle of the frame bundle which is a $GL(n)$-principal bundle. I guess this makes sense for equivariant injections along any Lie group homomorphism $G\to GL(n)$. The entry says something about spin structure, warning that the group $Spin(n)$ is not a subgroup of $GL(n)$. So what is meant ? The total space of a subbundle is a subspace at least. Does this mean that I consider the frame bundle first as a (non-principal) $Spin(n)$-bundle by pulling back along a fixed noninjective map $Spin(n)\to GL(n)$ and then I restrict to a chosen subspace on which the induced action of Spin group is principal ?

- Discussion Type
- discussion topicPierre Molino
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2020

brief

`category:people`

-entry for hyperlinking references at*G-structure*

- Discussion Type
- discussion topictangential structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2020

I am finally splitting this off from

*G-structure*. Have added comments on the disambiguation both here and there

- Discussion Type
- discussion topicTim Weelinck
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 18th 2020

brief

`category:people`

-entry for hyperlinking references at*factorization homology*and*orbifold*