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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 topicgraph product
- Category Latest Changes
- Started by Joe Moeller
- Comments 3
- Last comment by Joe Moeller
- Last Active Nov 18th 2019

- Discussion Type
- discussion topicmonoidal bicategory
- Category Latest Changes
- Started by Peter Heinig
- Comments 18
- Last comment by Joe Moeller
- Last Active Nov 18th 2019

One small question that has often occurred to me:

- in the three usual axioms specifying how the unit interacts with parenthesizing in a monoidal bicategory, is there any known reason for drawing one of the three diagrams as a square (as opposed to a triangle, like the other two) even though one of the 1-cells is the
*identity*id$\otimes$id, except for the (certainly important) aesthetical/visual/psychological reason that otherwise (if using the conventional notation) the tip of the arrow giving the 2-cell would point from a 1-cell to a 0-cell?

(Technical note: I chose the “Latest Changes” category, even though no change to monoidal bicategory was made yet, because monoidal bicategory appears to not have had a thread of its own yet, and it is not inconceivable that this page will evolve in the future and need a thread)

- in the three usual axioms specifying how the unit interacts with parenthesizing in a monoidal bicategory, is there any known reason for drawing one of the three diagrams as a square (as opposed to a triangle, like the other two) even though one of the 1-cells is the

- Discussion Type
- discussion topicNicolò Petri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2019

brief

`category:people`

-entry for hyperlinking references at*D6-D8 brane bound state*,*D2-D4 brane bound state*,*D4-D6 brane bound state*,*D2-D6 brane bound state*and*AdS/CFT*,*AdS3/CFT2*

- Discussion Type
- discussion topicGiuseppe Dibitetto
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2019

brief

`category:people`

-entry for hyperlinking references at*D6-D8 brane bound state*,*D2-D4 brane bound state*,*D4-D6 brane bound state*,*D2-D6 brane bound state*and*AdS/CFT*,*AdS3/CFT2*

- Discussion Type
- discussion topicD2-D6 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 18th 2019

- Discussion Type
- discussion topicElena Babalic
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2019

brief

`category:people`

-entry for hyperlinking references at*M-theory on 8-manifolds*and at*G-structure*

- Discussion Type
- discussion topicEran Palti
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2019

- Discussion Type
- discussion topicAndrei Micu
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 18th 2019

brief

`category:people`

-entry for hyperlinking references at*M-theory on Spin(7)-manifolds*and at*G-structure*

- Discussion Type
- discussion topicYang-Mills instanton
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 17th 2019

added to Yang-Mills instanton a discussion of instantons as tunnelings between Chern-Simons vacua.

- Discussion Type
- discussion topicFederico Bonetti
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2019

- Discussion Type
- discussion topicTim van Beek
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by RodMcGuire
- Last Active Nov 17th 2019

- Discussion Type
- discussion topicTom Pugh
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2019

- Discussion Type
- discussion topicfunction monad
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by nLab edit announcer
- Last Active Nov 17th 2019

created a minimum at

*function monad*(aka “reader monad”, “environment monad”)

- Discussion Type
- discussion topicAlexis Hazell
- Category Latest Changes
- Started by AlexisHazell
- Comments 9
- Last comment by Richard Williamson
- Last Active Nov 17th 2019

- Discussion Type
- discussion topicYang-Mills equation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2019

- Discussion Type
- discussion topicLaura Fredrickson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 17th 2019

brief

`category:people`

entry for hyperlinking references at*Yang-Mills theory*and*Yang-Mills equations*

- Discussion Type
- discussion topicstructured cospan
- Category Latest Changes
- Started by nLab edit announcer
- Comments 10
- Last comment by Joe Moeller
- Last Active Nov 16th 2019

This is my first (substantial) contribution to the nLab, so forgive my likely ineptitude. This wants to be a initial stub, everything is basically scraped from the reference and this post: https://golem.ph.utexas.edu/category/2019/07/structured_cospans.html Clearly a lot of material can be added, included a better definition and clearer examples. It’s also quite necessary to make a page for decorated cospans. I might start it myself later this month.

mattecapu

- Discussion Type
- discussion topicJules Hedges
- Category Latest Changes
- Started by Joe Moeller
- Comments 1
- Last comment by Joe Moeller
- Last Active Nov 16th 2019

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 41
- Last comment by Joe Moeller
- Last Active Nov 16th 2019

started a Properties-section at Lawvere theory with some basic propositions.

Would be thankful if some experts looked over this.

Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

- Discussion Type
- discussion topicadjoint functor theorem
- Category Latest Changes
- Started by John Baez
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Nov 16th 2019

I fixed a trivial typo in adjoint functor theorem but left wondering about this:

… the limit

$L c := \lim_{c\to R d} d$over the comma category $c/R$ (whose objects are pairs $(d,f:c\to R d)$ and whose morphisms are arrows $d\to d'$ in $D$ making the obvious triangle commute in $C$) of the projection functor

$L c = \lim_{\leftarrow} (c/R \to D ) \,.$I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit $L c$ over the comma category of the projection functor $L c$”, which would be circular. But it must be that both formulas are intended as synonymous definitions of $L c$. At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use $lim$ and $colim$ for limit and colimit.

I could probably guess how to fix this, but I won’t since I might screw something up.

- Discussion Type
- discussion topicproof net
- Category Latest Changes
- Started by Todd_Trimble
- Comments 13
- Last comment by Mike Shulman
- Last Active Nov 16th 2019

There has been a pretty massive expansion at proof net. All who are interested in this are invited to have a look (but the nLab is super-slow in loading now from where I write).

Noam Z., if you are reading this: I had looked at the notes you kindly mentioned to me recently. Could you comment on what the connection might be with the sequentialization result (see the remark 2 under theorem 1 in proof net)? The outline of proof reminded me of your description of inversion and focusing, but I confess I had a little trouble following everything (my fault, not yours).

- Discussion Type
- discussion topicF-theory on Spin(7)-manifolds
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 15th 2019

- Discussion Type
- discussion topicredshift
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

- Discussion Type
- discussion topicsupernova
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

- Discussion Type
- discussion topicWitten's Dark Fantasy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

am finally splitting this off as a stand-alone page (material used to be at

*cosmological constant*and at*F-theory*). Added a paragraph linking with*inhomogeneous cosmology*.

- Discussion Type
- discussion topicinhomogeneous cosmology
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Nov 15th 2019

started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective

- Discussion Type
- discussion topicMohamed Rameez
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

brief

`category:people`

-entry for hyperlinking references at*inhomogeneous cosmology*

- Discussion Type
- discussion topicHarvendra Singh
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

brief

`category:people`

-entry for hyperlinking references at*massive type IIA string theory*,*D8-brane*and*D6-D8-brane bound state*

- Discussion Type
- discussion topicisospin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

- Discussion Type
- discussion topicstrange quark
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 15th 2019

stub entry, to fill in

*flavors of fundamental particles – table*