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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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundations functional-analysis functor galois-theory 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 history homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory infinity integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology nonassociative 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 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 topicconnected space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 16
- Last comment by Todd_Trimble
- Last Active 6 days ago

I added a bunch of things to connected space: stuff on the path components functor, an example of a countable connected Hausdorff space, and the observation that the quasi-components functor is left adjoint to the discrete space functor $Set \to Top$ (Wikipedia reports that the connected components functor is left adjoint to the discrete space functor, but that’s wrong).

This bit about quasi-components functor had never occurred to me before, although it seems to be true. I’m having difficulty getting much information on this functor. For example, does it preserve finite products? I don’t know, but I doubt it. Does anyone reading this know?

- Discussion Type
- discussion topicCatLab
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Richard Williamson
- Last Active 6 days ago

Andre Joyal just created on the nLab an entry titled CatLab

- Discussion Type
- discussion topicspectral sequence of a filtered complex
- Category Latest Changes
- Started by jcmckeown
- Comments 13
- Last comment by Richard Williamson
- Last Active 6 days ago

new entry spectral sequence of a filtered complex, !included into the correct section of spectral sequence. Doubtless still needs tidying.

- Discussion Type
- discussion topiccharacter table of GL(2,3)
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Richard Williamson
- Last Active 6 days ago

- Discussion Type
- discussion topicsymmetric group
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicK-cohomology
- Category Latest Changes
- Started by David_Corfield
- Comments 8
- Last comment by Richard Williamson
- Last Active 6 days ago

K-cohomology is a strangely organised page with 5 sections identically named. There supposed to be some difference from K-theory

- Discussion Type
- discussion topicAtiyah-Segal completion theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active 7 days ago

stub for

*Atiyah-Segal completion theorem*, for the moment just to record a reference

- Discussion Type
- discussion topicBurnside ring
- Category Latest Changes
- Started by Todd_Trimble
- Comments 36
- Last comment by Urs
- Last Active 7 days ago

I added a Definition section to Burnside ring (and made Burnside rig redirect to it).

- Discussion Type
- discussion topiccyclotomic field
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active 7 days ago

I have created brief stubs for

*cyclotomic field*and*anti-cyclotomic field*. No real content there for the moment, just so as to make cross-links work and have a place to record references.I suppose what I am really looking for regarding discussion here in another thread is a concept of

*anti-cyclotomic spectrum*.

- Discussion Type
- discussion topiccyclotomic integer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicring of integers
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 7 days ago

needed to point to

*ring of integers*of a number field. The term used to redirect just to*integers*. I have split it off now with a minimum of content. Have to rush off now.

- Discussion Type
- discussion topicobservations on prime divisors of odd integers in a range
- Category Latest Changes
- Started by Richard Williamson
- Comments 38
- Last comment by Richard Williamson
- Last Active Oct 7th 2018

Hello all, I was wondering if one or two of you would be able to find the time to see if you think that the arguments on the following page, on my personal web, are correct? There are so many sharp minds amongst the readership here, that I’m sure if there is an error, one of you will make short work of finding it!

Observations on prime divisors of odd integers in a range (richardwilliamson)

With these kinds of elementary arguments, everything has to be exactly right; the entire argument is likely to collapse if the smallest detail is wrong. Thus, though I have checked the argument several times myself, including after having slept on it, it is eminently possible that I have overlooked something, so do read with a critical eye :-).

I am also thinking of making a little page, for completeness, on Bertrand’s postulate, on the main nLab, which I can link to in my argument. Would this be OK (I ask because I don’t know any category theoretic point of view on it at all)?

Any feedback will be greatly appreciated!

- Discussion Type
- discussion topicBridgeland stability condition
- Category Latest Changes
- Started by hilbertthm90
- Comments 33
- Last comment by David_Corfield
- Last Active Oct 6th 2018

There was an “Idea” at Bridgeland stability condition. I added the sections Definition, Key Results, and Examples. I also added a reference for the last key result listed. I should probably fill in some related stubs like t-structure or classical notions of stability.

- Discussion Type
- discussion topicGL(2,3)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 6th 2018

- Discussion Type
- discussion topiccharacter table of 2O
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Oct 6th 2018

- Discussion Type
- discussion topicTopos
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Oscar_Cunningham
- Last Active Oct 5th 2018

have added to Topos in the section on limits of toposes the description of the pullback of toposes by pushout of their sites of definition.

- Discussion Type
- discussion topiccharacter table of 2I
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 5th 2018

- Discussion Type
- discussion topicgolden ratio
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Oct 5th 2018

- Discussion Type
- discussion topic3-strand-braid-1-SVG
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Tim_Porter
- Last Active Oct 5th 2018

- Discussion Type
- discussion topicSegal completion -- table
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by David_Corfield
- Last Active Oct 5th 2018

table highlighting the pattern in the “Segal completion theorems”: Atiyah-Segal completion theorem and Segal-Carlsson completion theorem. Not a stand-alone entry, but for !inclusion into the various entries that the table relates to

- Discussion Type
- discussion topicbraid group
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Richard Williamson
- Last Active Oct 5th 2018

the entry

*braid group*said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).

- Discussion Type
- discussion topicmodal type theory
- Category Latest Changes
- Started by Urs
- Comments 77
- Last comment by David_Corfield
- Last Active Oct 5th 2018

created an entry

*modal type theory*; tried to collect pointers I could find to articles which discuss the interpretation of modalities in terms of (co)monads. I was expecting to find much less, but there are a whole lot of articles discussing this. Also cross-linked with*monad (in computer science)*.

- Discussion Type
- discussion topicgroup character
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 5th 2018

added to

*group character*brief remarks on

- Discussion Type
- discussion topicpermutation
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 4
- Last comment by Tim_Porter
- Last Active Oct 5th 2018

First attempt at a major revision of permutation that gives equal weight to the view of permutations-as-linear-orders, hoping that this article will eventually contain some discussion of the operad of permutations and of permutation patterns.

- Discussion Type
- discussion topicstring field theory
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Oct 5th 2018

I have started adding references to

*string field theory*, in particular those by Jim Stasheff et al. on the role of L-infinity algebra and A-infinity algebra. Maybe I find time later to add more details.

- Discussion Type
- discussion topicAndreas Dress
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 5th 2018

brief category:people-entry for hyperlinking references at

*permutation representation*

- Discussion Type
- discussion topicinternal logic
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Todd_Trimble
- Last Active Oct 4th 2018

created at internal logic an Examples-subsection and spelled out at Internal logic in Set how by turning the abstract-nonsense crank on the topos Set, one does reproduce the standard logic.

- Discussion Type
- discussion topicquaternion group
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Tim_Porter
- Last Active Oct 4th 2018

added the statement (here) that of all finite subgroups of $SU(2)$, $Q_8$ is a proper subgroup of the three exceptional ones.

Checking normality of this subgroup, I noticed that there is an issue with another item of the entry here, where it used to claim that a finite group is Hamiltonian precisely of it “contains a copy of $Q_8$”. But this can’t be, can it. I changed it to saying that every Hamiltonian group contains $Q_8$ as a subgroup, which I suppose is what was meant.

[edit: I see now that the statement that I changed back to was made already by Thomas Holder in rev 3, while the statement I removed was made by Thomas in rev 4. Thomas, if you see this, please let me know. ]

- Discussion Type
- discussion topicMatthew Weaver
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Oct 4th 2018

- Discussion Type
- discussion topicPermatuations and symmetric groups
- Category Latest Changes
- Started by TobyBartels
- Comments 4
- Last comment by Urs
- Last Active Oct 4th 2018

I found myself writing permutation (since I had linked to it) and realised that I could even redirect symmetric group there (which has been linked to for some time).

Pretty stubby now.