Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundle 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 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 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 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

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- Discussion Type
- discussion topictopos
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active Jan 22nd 2024

Added a table of contents to topos, a section on "special classes" and one on "higher toposes".

- Discussion Type
- discussion topicmonad
- Category Latest Changes
- Started by Urs
- Comments 99
- Last comment by Urs
- Last Active Jan 22nd 2024

following Zoran’s suggestion I added to the beginning of the Idea-section at monad a few sentences on the general idea, leading then over to the Idea with respect to algebraic theories that used to be the only idea given there.

Also added a brief stub-subsection on monads in arbitrary 2-categories. This entry deserves a bit more atention.

- Discussion Type
- discussion topicMarta Bunge
- Category Latest Changes
- Started by Tobias Fritz
- Comments 4
- Last comment by Urs
- Last Active Jan 22nd 2024

- Discussion Type
- discussion topicdependent type
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by nLab edit announcer
- Last Active Jan 22nd 2024

the entries

*dependent type*and*indexed set*did not know of each other.I have now cross-linked them minimally in their “Related entries”-sections. But this would deserve to be expanded on for exposition…

- Discussion Type
- discussion topicE7
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Jan 22nd 2024

added to

*E7*the statement of the decomposition of the smallest fundamental rep under $SL(8,\mathbb{R})$ and $SL(7,\mathbb{R})$ (here) and used this then to expand the existing paragraph on*As U-duality group of 4d SuGra*

- Discussion Type
- discussion topicMOND
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by nLab edit announcer
- Last Active Jan 21st 2024

recorded some recent surveys of the status of MOND at

*MOND*

- Discussion Type
- discussion topicMorse theory
- Category Latest Changes
- Started by David_Corfield
- Comments 6
- Last comment by perezl.alonso
- Last Active Jan 21st 2024

Added some references at Morse theory.

- Discussion Type
- discussion topicDirac charge quantization
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Jan 21st 2024

- Discussion Type
- discussion topicflexible limit
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active Jan 21st 2024

Add example of Eilenberg–Moore objects.

- Discussion Type
- discussion topicCMon-enriched symmetric monoidal category
- Category Latest Changes
- Started by J-B Vienney
- Comments 7
- Last comment by Urs
- Last Active Jan 21st 2024

- Discussion Type
- discussion topicconcept with an attitude
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Victor Sannier
- Last Active Jan 21st 2024

This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:

In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.

Here are examples:

A

*quiver*is just a directed graph (pseudograph, to be explicit). But one says*quiver*instead of*directed graph*when one is interested in studying*quiver representations*: functors from the free category on that graph to the category of finite-dimensional vector spaces.A

*presheaf*is just a contravariant functor. But one says*presheaf*instead of*contravariant functor*when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.

(…)

- Discussion Type
- discussion topicfree bicompletion
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicfree completion
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicquantum set
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 20th 2024

just a minimum for the moment, in order to record the definition in:

- Andre Kornell,
*Quantum Sets*, J. Math. Phys.**61**102202 (2020) [doi:10.1063/1.5054128]

- Andre Kornell,

- Discussion Type
- discussion topicMichael Mislove
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicdcpo
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by Urs
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicdomain
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicStefan Waldmann
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jan 20th 2024

- Discussion Type
- discussion topicde Rham theorem
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jan 20th 2024

mentioned the $A_\infty$-refinement at de Rham theorem

- Discussion Type
- discussion topicordinary homology
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 20th 2024

I needed a redirect-kind of entry

*ordinary homology*. So I created one.

- Discussion Type
- discussion topicmonoidal topos
- Category Latest Changes
- Started by spitters
- Comments 11
- Last comment by Urs
- Last Active Jan 19th 2024

- Discussion Type
- discussion topicAlvaro Restuccia
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 19th 2024

- Discussion Type
- discussion topicMaria P. Garcia del Moral
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 19th 2024

- Discussion Type
- discussion topictemporal logic
- Category Latest Changes
- Started by David_Corfield
- Comments 9
- Last comment by Victor Sannier
- Last Active Jan 19th 2024

I added a couple of references for the claim

There is a Curry–Howard correspondence between linear-time temporal logic (LTL) and functional reactive programming (FRP).

How about for CLT and CLT* (in the computation tree logic section)?

Were we looking to integrate this section with the one above on temporal type theory as an adjoint logic, could there be a way via some branching representation of our type $Time$ as a tree?

I see Joachim Kock has an interesting way of presenting trees.

- Discussion Type
- discussion topicstrong adjoint functor
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by maxsnew
- Last Active Jan 19th 2024

created strong adjoint functor

- Discussion Type
- discussion topicquantum gravity
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Jan 19th 2024

in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity

- Discussion Type
- discussion topicRiemannian geometry
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 19th 2024

added pointer to:

- John M. Lee,
*Riemannian manifolds. An introduction to curvature*. Graduate Texts in Mathematics 176 (1997), Springer. ISBN: 0-387-98271-X. Second Edition (retitled):*Introduction to Riemannian Manifolds*(2018), Springer. ISBN: 978-3-319-91754-2 (doi:10.1007/978-3-319-91755-9)

- John M. Lee,

- Discussion Type
- discussion topicOn the hypotheses which underlie geometry
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 19th 2024

- Discussion Type
- discussion topicRené Lavendhomme
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Tim_Porter
- Last Active Jan 19th 2024

- Discussion Type
- discussion topicAdams e-invariant
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by nLab edit announcer
- Last Active Jan 18th 2024

added rough description and original citation to

*Adams e-invariant*

- Discussion Type
- discussion topicfinal functor
- Category Latest Changes
- Started by Tom Hirschowitz
- Comments 17
- Last comment by BryceClarke
- Last Active Jan 18th 2024

- Discussion Type
- discussion topicHiggs field
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Urs
- Last Active Jan 18th 2024

added a brief historical comment to

*Higgs field*and added the historical references

- Discussion Type
- discussion topicskyrmion
- Category Latest Changes
- Started by Urs
- Comments 57
- Last comment by Urs
- Last Active Jan 18th 2024

- Discussion Type
- discussion topicYoichiro Nambu
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 18th 2024

- Discussion Type
- discussion topicEncyclopedia of Mathematical Physics 2nd ed
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Jan 18th 2024

starting a

`category:reference`

-entry.Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at

*Handbook of Quantum Gravity*and similar entries).I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.

- Discussion Type
- discussion topiclarge N limit
- Category Latest Changes
- Started by zskoda
- Comments 20
- Last comment by Urs
- Last Active Jan 18th 2024

We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.

- Discussion Type
- discussion topichigher curvature correction
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Jan 18th 2024

- Discussion Type
- discussion topicfixed point
- Category Latest Changes
- Started by Todd_Trimble
- Comments 21
- Last comment by varkor
- Last Active Jan 17th 2024

Made a start on an article fixed point, which might need to be farmed out to “sub-pages” (as this is a mighty big general topic).

- Discussion Type
- discussion topicentwining structure
- Category Latest Changes
- Started by zskoda
- Comments 16
- Last comment by mattecapu
- Last Active Jan 17th 2024

Cleaning or creating entries related to corings (e.g. grouplike element, Sweedler coring) and entwining structures, including personal entries Gabriella Böhm, Tomasz Brzeziński etc. On the edge of this activity I am interested in the relation between classical correspondence between flat connections and the descent data in abelian context; it could be related to the theorem of Urs and Konrad on the relation between descent data and transport functors in global context. I would like to know the parallel precisely.

- Discussion Type
- discussion topicalgebra for a profunctor
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Jan 17th 2024

Added a cross-reference to algebra for an endomorphism.

- Discussion Type
- discussion topicfield with one element
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active Jan 17th 2024

created field with one element with two useful references

- Discussion Type
- discussion topicreal numbers type
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jan 16th 2024

- Discussion Type
- discussion topicdouble category
- Category Latest Changes
- Started by John Baez
- Comments 26
- Last comment by varkor
- Last Active Jan 16th 2024

- I added more info on pseudo double categories and double bicategories to double category. I also simplified the picture of a square, which had been bristling with scary unnecessary detail. There's a slight blemish in the left vertical arrow, which I can't see how to fix.

- Discussion Type
- discussion topicSpin(7) manifold
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jan 16th 2024

added this statement:

Let $X$ be a closed smooth manifold of dimension 8 with Spin structure. If the frame bundle moreover admits G-structure for

$G = Spin(7) \hookrightarrow Spin(8)$then the Euler class $\chi$, the second Pontryagin class $p_2$ and the cup product-square $(p_1)^2$ of the first Pontryagin class of the frame bundle/tangent bundle are related by

$8 \chi \;=\; 4 p_2 - (p_1)^2 \,.$

- Discussion Type
- discussion topicKosta Došen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 16th 2024

- Discussion Type
- discussion topicM-Theory and Mathematics
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Jan 15th 2024

- Discussion Type
- discussion topicmoduli spaces -- contents
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 15th 2024

- Discussion Type
- discussion topicclan
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by nLab edit announcer
- Last Active Jan 15th 2024

- Discussion Type
- discussion topichomological category
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Ali Caglayan
- Last Active Jan 14th 2024

New entry homological category.

- Discussion Type
- discussion topicchange of enriching category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by nLab edit announcer
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicIan Putnam
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicC-star-algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topiccontinuous field of C*-algebras
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 14th 2024

brief note on

*continuous field of C*-algebras*

- Discussion Type
- discussion topicSimon Wassermann
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicEberhard Kirchberg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicGelfand-Naimark-Segal construction
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicCauchy–Schwarz inequality
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 4
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicsigned graph
- Category Latest Changes
- Started by Zaslav
- Comments 2
- Last comment by Urs
- Last Active Jan 14th 2024

- Discussion Type
- discussion topicchromatic homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Jan 14th 2024

I gave

*chromatic homotopy theory*an Idea-section.To be expanded eventually…

- Discussion Type
- discussion topicConway's game of life
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 14th 2024

Stub entry, for the moment just to have a ace for recording this result:

Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich, Matthias Merzenich, David Raucci, Mitchell Riley,

*Conway’s Game of Life is Omniperiodic*[arXiv:2312.02799]The Physics arXiv Blog,

*Mathematicians Prove the “Omniperiodicity” of Conway’s Game of Life*(Dec 2024)