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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-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions 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 goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage 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 superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topicbracket type
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by nLab edit announcer
- Last Active Nov 28th 2018

started bracket type, just for completeness, but don’t really have time for it

- Discussion Type
- discussion topicrepresentation theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Nov 27th 2018

gave

*representation theory*a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over $\mathbf{B}G$ and added the following*homotopy type representation theory – table*, which I am also including in other relevant entries:homotopy type theory representation theory pointed connected context $\mathbf{B}G$ ∞-group $G$ dependent type ∞-action/∞-representation dependent sum along $\mathbf{B}G \to \ast$ coinvariants/homotopy quotient context extension along $\mathbf{B}G \to \ast$ trivial representation dependent product along $\mathbf{B}G \to \ast$ homotopy invariants/∞-group cohomology dependent sum along $\mathbf{B}G \to \mathbf{B}H$ induced representation context extension along $\mathbf{B}G \to \mathbf{B}H$ dependent product along $\mathbf{B}G \to \mathbf{B}H$ coinduced representation

- Discussion Type
- discussion topicnerve
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Nov 27th 2018

- Discussion Type
- discussion topicclassifying topos for the theory of objects
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by DavidRoberts
- Last Active Nov 27th 2018

I have splitt off from

*classifying topos*an entry*classifying topos for the theory of objects*and added the statement about the relation to finitary monads.

- Discussion Type
- discussion topiclocale
- Category Latest Changes
- Started by barakat
- Comments 34
- Last comment by nLab edit announcer
- Last Active Nov 27th 2018

- The way of writing the adjunction in locale in Prop 4. and Corollary 1. is a bit misleading: When you explicit the adjunction symbol you normally write the domain of the right adjoint on the left and its codomain on the right (e.g., as in reflective subcategory). I didn't do the change myself as I might be missing a convention here.

- Discussion Type
- discussion topiccartesian theory > history
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Nov 27th 2018

This page should be merged with “essentially algebraic theory”, as the two notions are equivalent. Since the “cartesian theory” has little in it, I’m attempting to redirect to “essentially algebraic theory”. There is also relevant stuff at “cartesian logic”, though I’m not sure how best to organize that and link to it.

Steve Vickers

- Discussion Type
- discussion topicessentially algebraic theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Nov 27th 2018

added references to

*essentially algebraic theory*. Also equipped the text with a few more hyperlinks.

- Discussion Type
- discussion topicgeometric theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 32
- Last comment by nLab edit announcer
- Last Active Nov 27th 2018

Added a description of several different approaches to geometric theory.

- Discussion Type
- discussion topicgeometric quantization
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Nov 27th 2018

started an Examples-section at geometric quantization

- Discussion Type
- discussion topicRobert Penner
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 27th 2018

brief category:people entry for hyperlinking references at

*super Riemann surface*

- Discussion Type
- discussion topicsuper Riemann surface
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 27th 2018

created a stub for

*super Riemann surface*, just to record Witten’s latest

- Discussion Type
- discussion topicblack hole in anti-de Sitter spacetime
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 27th 2018

- Discussion Type
- discussion topicquantum geometric Langlands correspondence
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 27th 2018

started quantum geometric Langlands correspondence with a summary of some basics from Frenkel’s notes

- Discussion Type
- discussion topicAdS-CFT in condensed matter physics
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 27th 2018

- Discussion Type
- discussion topicconfinement
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Nov 27th 2018

stub for

*confinement*, but nothing much there yet. Just wanted to record the last references there somewhere.

- Discussion Type
- discussion topicpropositional logic
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Nov 26th 2018

- Discussion Type
- discussion topicgeometric type theory
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Nov 26th 2018

I came to think that the term

*geometric type theory*for the type theory internal toi sheaf toposes should exists. Thanks to Bas Spitter for pointing out that Steve Vickers had already had the same idea (now linked to at the above entry).Also created

*geometric homotopy type theory*in this vein, with some evident comments.

- Discussion Type
- discussion topiccartesian logic
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Nov 26th 2018

- Discussion Type
- discussion topicRoger Penrose
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_Porter
- Last Active Nov 26th 2018

added some actual text to the category:people entry

*Roger Penrose*

- Discussion Type
- discussion topiccategory of group-based universal algebras
- Category Latest Changes
- Started by Tim_Porter
- Comments 23
- Last comment by Mike Shulman
- Last Active Nov 26th 2018

- Discussion Type
- discussion topic(infinity,1)-category of (infinity,1)-presheaves
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Alizter
- Last Active Nov 26th 2018

It would be nice if the entry were a little more explicit about the slicing theorem

$PSh_\infty(\mathcal{C}_{/p}) \stackrel{\simeq}{\to} PSh_\infty(\mathcal{C})_{/y p} \,.$(here)

In the special case that the small $\infty$-category $\mathcal{C}$ happens to be a small $\infty$-groupoid and that $p$ is constant on an object $X \in \mathcal{C}$, it ought to be true that an explicit form of this equivalence is given in semi-HoTT notation by

$\left( (c \overset{\gamma}{\to}X) \;\mapsto\; \mathcal{F}(\gamma) \right) \;\mapsto\; \left( c \;\mapsto\; \array{ \underset{c \underset{\gamma}{\to}X}{\sum} \mathcal{F}(\gamma) \\ \downarrow \\ \underset{c \underset{\gamma}{\to}X}{\sum} \ast } \right) \,.$This must be an easy theorem in HoTT?

- Discussion Type
- discussion topicexplicit substitution
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Nov 26th 2018

- Discussion Type
- discussion topicmonad (in linguistics)
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by David_Corfield
- Last Active Nov 25th 2018

- Discussion Type
- discussion topicOmega-group
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Nov 25th 2018

- Discussion Type
- discussion topicGoodwillie derivative of the identity functor
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Nov 23rd 2018

- Discussion Type
- discussion topicGoodwillie chain rule
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Nov 23rd 2018

- Discussion Type
- discussion topicsupergeometry
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Nov 23rd 2018

added to supergeometry a link to the recent talk

- Mikhail Kapranov,
*Categorification of supersymmetry and stable homotopy groups of spheres*(video)

- Mikhail Kapranov,

- Discussion Type
- discussion topicArthur Wasserman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2018

brief category:people-entry for the purpose of hyperlinking references at

*equivariant cohomotopy*

- Discussion Type
- discussion topicflavours of cohomotopy -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2018

- Discussion Type
- discussion topicequivariant cohomotopy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 22nd 2018

am starting something here. For the moment I just want to record today’s

- Daniel Grady,
*Cobordisms of global quotient orbifolds and an equivariant Pontrjagin-Thom construction*(arXiv:1811.08794)

eventually more references ought to be added

- Daniel Grady,