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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion 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 foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 k-theory lie-theory 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 nforum 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 set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string 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 topicmonoidal functor
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by nLab edit announcer
- Last Active Mar 27th 2024

created (finally) lax monoidal functor (redirecting monoidal functor to that) and strong monoidal functor.

Hope I got the relation to 2-functors right. I remember there was some subtlety to be aware of, but I forget which one. I could look it up, but I guess you can easily tell me.

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 109
- Last comment by nLab edit announcer
- Last Active Mar 27th 2024

Todd,

when you see this here and have a minute, would you mind having a look at

*monoidal category*to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?Thanks!

- Discussion Type
- discussion topicpro-étale morphism of schemes
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Mar 27th 2024

- Discussion Type
- discussion topicBethe ansatz
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 26th 2024

- Discussion Type
- discussion topicBlake Stacey
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Mar 26th 2024

- Discussion Type
- discussion topicBott connection
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Mar 26th 2024

- Discussion Type
- discussion topicflat module
- Category Latest Changes
- Started by Andrew Stacey
- Comments 45
- Last comment by dmjc
- Last Active Mar 25th 2024

I’ve made a few changes at flat module since I wanted to know what one was and the nLab page simply confused me further. It seemed to be saying that a module over a ring/algebra $A$ is flat if tensoring

**with $A$**is a flat functor. That seemed absurd so I changed it. The observation “everything happens for a reason” was a little curt so once I’d worked out what it meant I expanded it a bit and put in the analogy to bases. It wasn’t clear from the way that it was phrased whether this condition was due to Wraith and Blass or the fact that it can be put in a more general context. Lastly, the last sentence was originally in the same paragraph as the penultimate sentence where it didn’t seem to fit (or was at best ambiguous) and it also claimed that the module could be non-unital which seemed a little odd.If an expert could kindly check that I’ve done no lasting damage to the page, I’d be grateful.

- Discussion Type
- discussion topicde Sitter spacetime
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 25th 2024

added pojnter to Maldacena-Nunez 01

- Discussion Type
- discussion topicfirst-order formulation of gravity
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 24th 2024

I have touched the Idea-section at

*first-order formulation of gravity*, trying to improve a little.

- Discussion Type
- discussion topicstrict 2-group
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Mark John Hopkins
- Last Active Mar 24th 2024

considerably expanded the entry strict 2-group.

Apart from adding an introductory discussion, and expanding the list of examples, in particular by adding that of automorphism 2-groups ...

... I in particular give the detailed translation prescription for how to encode a 2-group by a crossed module at In terms of crossed modules

This is to eventually serve as a supplement to the discussion at nonabelian group cohomology. So I spent some energy on disentangling the four different (though isomorphic) ways a crossed module gives rise to a 2-group (following my article with David Roberts).

- Discussion Type
- discussion topiclist of journals publishing homotopy theory and category theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 74
- Last comment by Mike Shulman
- Last Active Mar 22nd 2024

- Discussion Type
- discussion topicGalois category
- Category Latest Changes
- Started by Richard Williamson
- Comments 3
- Last comment by nLab edit announcer
- Last Active Mar 22nd 2024

- Discussion Type
- discussion topicComptes rendus hebdomadaires des séances de l'Académie des sciences
- Category Latest Changes
- Started by varkor
- Comments 15
- Last comment by varkor
- Last Active Mar 22nd 2024

- Discussion Type
- discussion topiclens (in computer science)
- Category Latest Changes
- Started by David_Corfield
- Comments 60
- Last comment by varkor
- Last Active Mar 22nd 2024

- Discussion Type
- discussion topicDeligne tensor product of abelian categories
- Category Latest Changes
- Started by John Baez
- Comments 4
- Last comment by John Baez
- Last Active Mar 21st 2024

I edited

to make it clear that this tensor product only works for

*finite*abelian categories, which are what we get from looking at*finite-dimensional*representations of*finite-dimensional*associative algebras. It’s all very finite… and over fields, too, at least in the treatment by Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik, which is all I have access to now. It would be nice to see this kind of thing done more generally. The slides by Ignacio López Franco, linked on this page, are a hint of how to do it.

- Discussion Type
- discussion topicorthocompact space
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by Urs
- Last Active Mar 21st 2024

Created bare minimum for orthocompact, which will be expanded later.

Edit: I’m not sure if there is a convention for the title? With or without “topological”? One one hand there are compact space, metacompact space or hemicompact space. On the other hand, there are locally compact topological space or paracompact topological space.

Edit: I’ve now linked orthocompace space on hemicompact space and paracompact topological space as there are lemmata connecting them with each other.

- Discussion Type
- discussion topicWeinstein symplectic category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by perezl.alonso
- Last Active Mar 21st 2024

started

*Weinstein symplectic category*

- Discussion Type
- discussion topicrational homotopy sphere
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Mar 21st 2024

- Discussion Type
- discussion topicrational homology sphere
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Mar 21st 2024

Created bare minimum for rational homology sphere, which will be expanded later.

- Discussion Type
- discussion topichomotopy sphere
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Samuel Adrian Antz
- Last Active Mar 21st 2024

- Discussion Type
- discussion topicspheres -- contents
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 21st 2024

- Discussion Type
- discussion topichomology sphere
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Samuel Adrian Antz
- Last Active Mar 21st 2024

- Discussion Type
- discussion topicAbdus Salam
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 21st 2024

added pointer to today’s:

- Peter West:
*Memories of Abdus Salam and the early days of supersymmetry*[arXiv:2403.13453]

- Peter West:

- Discussion Type
- discussion topicmetrisable topological space
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 3
- Last comment by ʇɐ
- Last Active Mar 20th 2024

- Discussion Type
- discussion topicG-delta subspace
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by ʇɐ
- Last Active Mar 20th 2024

Added Mazurkiewicz theorem and Hausdorff Gδ theorem with original reference by Stefan Mazurkiewicz and Felix Hausdorff. Linked english Wikipedia page. (The german Wikipedia page is now also available.)

- Discussion Type
- discussion topicKan fibration
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Hurkyl
- Last Active Mar 20th 2024

added the pointers to the combinatorial proofs of the fiberwise detection of acyclicity of Kan fibrations, currently discussed on the AlgTop list, to the nLab here.

- Discussion Type
- discussion topicvector bundle
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by perezl.alonso
- Last Active Mar 20th 2024

at

*vector bundle*I have spelled out the proof that for $X$ paracompact Hausdorff then the restrictions of vector bundles over $X \times [0,1]$ to $X \times \{0\}$ and $X \times \{1\}$ are isomorphic.It’s just following Hatcher, but I wanted to give full detail to the argument of what is now this lemma.

- Discussion Type
- discussion topicP-space
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Mar 20th 2024

Created page for P-space. (I intend to create the page for orthocompact spaces in the future. The german Wikipedia page is now also available.)

- Discussion Type
- discussion topicStefan Mazurkiewicz
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 2
- Last comment by Urs
- Last Active Mar 20th 2024

Created page for Stefan Mazurkiewicz with reference of the Mazurkiewicz theorem both featured on G-delta subspace.

- Discussion Type
- discussion topicAdS-CFT correspondence
- Category Latest Changes
- Started by Urs
- Comments 38
- Last comment by rohan02
- Last Active Mar 20th 2024

- Discussion Type
- discussion topicN. S. Baaklini
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 20th 2024

- Discussion Type
- discussion topicD'Auria-Fré-Regge formulation of supergravity
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Mar 20th 2024

crated D'Auria-Fre formulation of supergravity

there is a blog entry to go with this here

- Discussion Type
- discussion topicBenjamin McKay
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 20th 2024

- Discussion Type
- discussion topicCartan geometry
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 20th 2024

added this quote to before the Idea-section:

In the wake of the movement of ideas which followed the general theory of relativity, I was led to introduce the notion of new geometries, more general than Riemannian geometry, and playing with respect to the different Klein geometries the same role as the Riemannian geometries play with respect to Euclidean space. The vast synthesis that I realized in this way depends of course on the ideas of Klein formulated in his celebrated Erlangen programme while at the same time going far beyond it since it includes Riemannian geometry, which had formed a completely isolated branch of geometry, within the compass of a very general scheme in which the notion of group still plays a fundamental role.

[Élie Cartan 1939, as quoted in Sharpe 1997, p. 171]

- Discussion Type
- discussion topicEfimov K-theory
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 4
- Last comment by Dmitri Pavlov
- Last Active Mar 20th 2024

## Idea

A generalization of Waldhausen K-theory to dualizable dg-categories and dualizable stable ∞-categories.

For compactly generated inputs, recovers the Waldhausen K-theory of the full subcategory of compact objects.

The formalism is applicable to $\lambda$-presentable stable ∞-categories, where $\lambda$ can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis).

## References

Alexander Efimov,

*On the K-theory of large triangulated categories*, ICM 2022, https://www.youtube.com/watch?v=RUDeLo9JTroMarc Hoyois,

*K-theory of dualizable categories (after A. Efimov)*, https://hoyois.app.uni-regensburg.de/papers/efimov.pdf.Li He,

*Efimov K-theory and universal localizing invariant*, arXiv:2302.13052.

- Discussion Type
- discussion topiciterated algebraic K-theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by perezl.alonso
- Last Active Mar 19th 2024

- Discussion Type
- discussion topicstring theory FAQ
- Category Latest Changes
- Started by Urs
- Comments 79
- Last comment by nLab edit announcer
- Last Active Mar 19th 2024

added to

*string theory FAQ*two new paragraphs:Prompted by the MO discussion

- Discussion Type
- discussion topiclattice gauge theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 16
- Last comment by nLab edit announcer
- Last Active Mar 19th 2024

- Discussion Type
- discussion topiccompactly assembled (∞,1)-category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 0
- Last comment by Urs
- Last Active Mar 19th 2024

- Discussion Type
- discussion topiclinearly distributive category
- Category Latest Changes
- Started by Mike Shulman
- Comments 34
- Last comment by Mike Shulman
- Last Active Mar 19th 2024

I reorganized linearly distributive category by moving the long block of history down to the bottom, adding an “Idea” section and a description of how $*$-autonomous categories give rise to linearly distributive ones and linearly distributive ones give rise to polycategories. I also cross-linked the page better with polycategory and star-autonomous category.

- Discussion Type
- discussion topiccompactly generated (∞,1)-category
- Category Latest Changes
- Started by Hurkyl
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Mar 18th 2024

- Discussion Type
- discussion topicdistributivity of limits over colimits
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 14
- Last comment by Dmitri Pavlov
- Last Active Mar 18th 2024

- Discussion Type
- discussion topictopologically twisted D=4 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by perezl.alonso
- Last Active Mar 18th 2024

started

*topologically twisted D=4 super Yang-Mills theory*, in order to finally write a reply to that MO question we were talking about. But am being interrupted now…

- Discussion Type
- discussion topicPeano arithmetic
- Category Latest Changes
- Started by Todd_Trimble
- Comments 7
- Last comment by nLab edit announcer
- Last Active Mar 18th 2024

I added some material to Peano arithmetic and Robinson arithmetic. At the latter, I replaced the word “fragment” (which sounds off to my ears – actually Wikipedia talks about thisterm a little) with “weakening”.

Still some links to be inserted.

- Discussion Type
- discussion topicconfluent category
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by Alexander
- Last Active Mar 18th 2024

- Discussion Type
- discussion topicpseudomonic functor
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 18th 2024

- Discussion Type
- discussion topicJohnstone's topological topos
- Category Latest Changes
- Started by spitters
- Comments 3
- Last comment by nLab edit announcer
- Last Active Mar 18th 2024

- Discussion Type
- discussion topicno boundary proposal
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 18th 2024

added some minimum of content to this stub entry, including pointer to today’s

- Juan Maldacena,
*Comments on the no boundary wavefunction and slow roll inflation*[arXiv:2403.10510]

- Juan Maldacena,

- Discussion Type
- discussion topicinfrared divergence
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Mar 18th 2024

added pointer to yesterday’s

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

- Paweł Duch,

- Discussion Type
- discussion topicexterior algebra
- Category Latest Changes
- Started by sgarush
- Comments 5
- Last comment by Urs
- Last Active Mar 17th 2024

- Discussion Type
- discussion topicSergei M. Kuzenko
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2024

- Discussion Type
- discussion topicIoseph L. Buchbinder
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2024

- Discussion Type
- discussion topicsuperspace
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active Mar 17th 2024

completed publication data for:

- Abdus Salam, John Strathdee,
*Superfields and Fermi-Bose symmetry*, Physical Review D11, 1521-1535 (1975) (doi:10.1142/9789812795915_0051)

- Abdus Salam, John Strathdee,

- Discussion Type
- discussion topicCartan structural equations and Bianchi identities -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2024

a bare list of references, to be

`!include`

-ed into the References-sections of relevant entries (such as as*Cartan structural equations*,*Bianchi identities*,*Cartan connection*etc.)

- Discussion Type
- discussion topicCartan structural equations
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2024

- Discussion Type
- discussion topicErhard Scholz
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 17th 2024

- Discussion Type
- discussion topiccombinatorial category
- Category Latest Changes
- Started by varkor
- Comments 7
- Last comment by varkor
- Last Active Mar 17th 2024

- Discussion Type
- discussion topicdifferential geometry
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Urs
- Last Active Mar 16th 2024

have expanded the single sentence at differential geometry to something like a paragraph, indicating how differential geometry is the “higher geometry modeled on the pre-geometry $\mathcal{G} = CartSp$”

- Discussion Type
- discussion topicAndrzej Derdzinski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 16th 2024

- Discussion Type
- discussion topichigher curvature corrections to D=11 supergravity -- references
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 16th 2024

a bare list of references, previously coded both at

*D=11 supergravity*and at*higher curvature correction*, now extracted here to be`!include`

-ed back there, for ease of synchronizing