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- Discussion Type
- discussion topiclocale
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Guest
- Last Active 4 hours ago

added to locale a section relation to toposes stating localic reflection

- Discussion Type
- discussion topicStiefel manifold
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Todd_Trimble
- Last Active 5 hours ago

I have added some minimum content to

*Stiefel manifold*, also a little bit to*Grassmannian*

- Discussion Type
- discussion topiccompact object
- Category Latest Changes
- Started by Mike Shulman
- Comments 4
- Last comment by Todd_Trimble
- Last Active 6 hours ago

- Discussion Type
- discussion topicbi-
- Category Latest Changes
- Started by varkor
- Comments 4
- Last comment by J-B Vienney
- Last Active 6 hours ago

- Discussion Type
- discussion topicmodel structure on simplicial groupoids
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active 10 hours ago

weirdly, this page never linked to

*simplicial groupoid*. I am adjusting a little…

- Discussion Type
- discussion topicdiscrete category
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active 10 hours ago

- Discussion Type
- discussion topicHopf monad
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by varkor
- Last Active 11 hours ago

Added to Hopf monad the Bruguières-Lack-Virelizier definition and some properties.

- Discussion Type
- discussion topicpushout
- Category Latest Changes
- Started by John Baez
- Comments 11
- Last comment by Urs
- Last Active 12 hours ago

I made some minor improvements to the Properties section of pushout, making it match the similar section in pullback insofar as it can. (It’s a bit tiring to have to look at both these pages to get all the basic properties, so I fixed that, but for properties that hold both for pullbacks and dually for pushouts I’m happy to have all the proofs at pullback - that’s how it works now.)

- Discussion Type
- discussion topicfree groupoid
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 12 hours ago

I have touched the formatting at

*free groupoid*. Then I added the statement that the fundamental groups of a free groupoid are free. Also added a pointer to a writeup of the proof.

- Discussion Type
- discussion topicmodel structure on sSet-categories
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active 12 hours ago

started adding some genuine substance to model structure on sSet-categories (which used to be just a template).

- Discussion Type
- discussion topicmodel structure for quasi-categories
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active 13 hours ago

added some basics to

*model structure for quasi-categories*at*general properties*

- Discussion Type
- discussion topicRoss Street
- Category Latest Changes
- Started by Tim_Porter
- Comments 27
- Last comment by BryceClarke
- Last Active 15 hours ago

As there had been a change to the entry for Ross Street I gave it a glance. Is there a reason that the second reference is to a paper without Ross as an author?I hesitate to delete it as there may be a hidden reason. (I have edited this discussion entry to remedy the point that Todd and Urs have made below. I also edited the title of this discussion!)

- Discussion Type
- discussion topicambidextrous adjunction
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by varkor
- Last Active 15 hours ago

started a stub for

*ambidextrous adjunction*, but not much there yet

- Discussion Type
- discussion topic[[lawvere interval]]
- Category Latest Changes
- Started by Harry Gindi
- Comments 9
- Last comment by jonsterling
- Last Active 16 hours ago

I stated this for presheaf categories, but I’m pretty sure that it carries over for any Grothendieck topos.

Check it out: lawvere interval

- Discussion Type
- discussion topicLawvere interval
- Category Latest Changes
- Started by jonsterling
- Comments 1
- Last comment by jonsterling
- Last Active 16 hours ago

- Discussion Type
- discussion topicn-category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active 16 hours ago

When pointing somebody to it, I noticed that the entry

*n-category*is in a rather sad state and in particular it used to start out in a rather unhelpful fashion. I have now tried to briefly fix at least the latter problem by expanding and editing the first two sentences a bit. Notably I made sure that a pointer to*(∞,n)-category*appears early on, for that is a place with more robust information, currently.

- Discussion Type
- discussion topicDwyer-Kan fundamental simplicial groupoid
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active 20 hours ago

I have adjusted and expanded wording and formatting in this entry.

Notice that the definition of the source and target maps that was (and still is) given here differs from that in Dwyer & Kan (1984):

where Dwyer & Kan’s §3.1(ii) “discards vertices from the right”, the definition that was (and still is) given in the entry seems to want to switch to the convention where vertices are discarded “from the left”.

With due care this can probably be made an equivalent definition, but as currently stated

$s = (d_1)^{n+1}$

$t = d_0(d_2)^n$

this must be wrong in itself: the “$d_2$” probably wants to be a “$d_1$”.

If anyone wants to fix this, feel invited. Otherwise I’ll change this to Dwyer & Kan’s definition.

- Discussion Type
- discussion topicrigidification of quasi-categories
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 20 hours ago

- Discussion Type
- discussion topicrelation between quasi-categories and simplicial categories
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active 22 hours ago

one more remark at relation between quasi-categories and simplicial categories

(to be expanded...)

- Discussion Type
- discussion topichigher-order logic
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Hugo Herbelin
- Last Active 1 day ago

- Discussion Type
- discussion topiccompactly generated topological space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 88
- Last comment by Todd_Trimble
- Last Active 1 day ago

I left a counter-query underneath Zoran’s query at compactly generated space. It may be time for a clean-up of this article; the query boxes have been left dangling and unanswered for quite some time. Either proofs or references to detailed proofs would be welcome.

- Discussion Type
- discussion topicpower series
- Category Latest Changes
- Started by nLab edit announcer
- Comments 10
- Last comment by Todd_Trimble
- Last Active 1 day ago

- Discussion Type
- discussion topictraced monoidal category
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by J-B Vienney
- Last Active 1 day ago

created

*traced monoidal category*with a bare minimumI would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.

- Discussion Type
- discussion topicrelative monad
- Category Latest Changes
- Started by mattecapu
- Comments 14
- Last comment by BryceClarke
- Last Active 1 day ago

- Discussion Type
- discussion topicsemi-simplicial types in homotopy type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 15
- Last comment by Hugo Herbelin
- Last Active 1 day ago

- Discussion Type
- discussion topicbimodule
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Todd_Trimble
- Last Active 1 day ago

I noticed only now that the entry

*bimodule*is in bad shape and needs some attention. For the moment I have added here a mentioning of the 2-category of algebras, bimodules and intertwiners and a pointer to the Eilenberg-Watts theorem.

- Discussion Type
- discussion topiccyclic set
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by zskoda
- Last Active 1 day ago

Have added to

*cyclic set*a pointer to notes from 1996 by Ieke Moerdijk where the theory classified by the topos of cyclic sets is identified (abstract circles).This is an unpublished note, but on request I have now uploaded it to the nLab

- Ieke Moerdijk,
*Cyclic sets as a classifying topos*, 1996 (pdf)

I have also added a corresponding brief section to

*classifying topos*.By the way, there is an old query box with an exchange between Mike and Zoran at

*cyclic set*. It seems to me that this has been resolved and the query box could be removed (to make the entry read more smoothly). Maybe Mike and/or Zoran could briefly look into this.- Ieke Moerdijk,

- Discussion Type
- discussion topicmodule over a monoid
- Category Latest Changes
- Started by J-B Vienney
- Comments 1
- Last comment by J-B Vienney
- Last Active 2 days ago

- Discussion Type
- discussion topicIntroduction to Topology -- 1
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Guest
- Last Active 2 days ago

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 51
- Last comment by varkor
- Last Active 2 days ago

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 topicreal quadratic function
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by Guest
- Last Active 2 days ago

- Discussion Type
- discussion topicleft division in modal type theory
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by Todd_Trimble
- Last Active 2 days ago

- Discussion Type
- discussion topicinverse Galois problem
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 5
- Last comment by Urs
- Last Active 2 days ago

I created inverse Galois problem. However as it stand this stub does not meet nlab standards since it doesn’t refer to category theory.

- Discussion Type
- discussion topicquantum error correction
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicAndreas Wallraff
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicMarkus Müller
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicsimplicial groupoid
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 3 days ago

added looping/delooping statements to model structure on simplicial groupoids and model structure on presheaves of simplicial groupoids.

**Question**: Suppose we take the catgeory of genuine simplicial groupoids $Grpd^\Delta$ (no restriction on the simplicial set of objects). Does $\bar W : Grpd^\Delta \to sSet$ send degreewise fibrations to fibrations?

- Discussion Type
- discussion topicAzumaya algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by John Baez
- Last Active 3 days ago

earlier today I had added at

*Azumaya algebra*a new section*In terms of (derived) étale cohomology*with some notes that I took during a talk by David Gepner. He has a quite beautiful picture. Maybe I find the time to expand a bit on this entry and related entries.

- Discussion Type
- discussion topicintegral
- Category Latest Changes
- Started by zskoda
- Comments 14
- Last comment by Guest
- Last Active 3 days ago

Urs has added Euler integration prompted by Tom’s post at nCafe; I wanted to do that and will contribute soon. I noticed there is no entry integral in $n$Lab, but it redirects to integration. I personally think that integral as a mathematical object is a slightly more canonical name for a mathematical entry than integration, if the two are not kept separated. Second, the entry is written as an (incomplete) disambiguation entry and with a subdivision into measure approach versus few odd entries. I was taught long time ago by a couple of experts in probability and measure theory that a complete subordination to the concept of integral to a concept of measure is pedagogically harmful, and lacks some important insights. This has also to do with the choice of the title: integration points to a process, and the underlying process may involve measure. Integral is about an object which is usually some sort of functional, or operator, on distributions which are to be acted upon.

Thus I would like to rename the entry into integral (or to create a separate entry from integration) and make it into a real entry, the list of variants being just a section, unlike in the disambiguation only version. What do you think. Then I would add some real ideas about it.

- Discussion Type
- discussion topicDarboux integration
- Category Latest Changes
- Started by Guest
- Comments 1
- Last comment by Guest
- Last Active 3 days ago

- Discussion Type
- discussion topicinvertible field theory
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicp-adic Teichmüller theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active 3 days ago

- Discussion Type
- discussion topiccategory of elements
- Category Latest Changes
- Started by Mike Shulman
- Comments 2
- Last comment by hugopaquet
- Last Active 3 days ago

I added to category of elements an argument for why $El$ preserves colimits.

- Discussion Type
- discussion topicKurusch Ebrahimi-Fard
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicassociative dialgebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicdendriform algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicTornike Kadeishvili
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicKirti Joshi
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 3 days ago

brief

`category:people`

-entry for satisfying links now requested at*p-adic Teichmüller theory*

- Discussion Type
- discussion topicbrace algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicnoncommutative differential calculus
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by zskoda
- Last Active 3 days ago

New entry noncommutative differential calculus with redirect Batalin-Vilkovisky module.

- Discussion Type
- discussion topicflexible limit
- Category Latest Changes
- Started by varkor
- Comments 2
- Last comment by varkor
- Last Active 3 days ago

Add example of Eilenberg–Moore objects.

- Discussion Type
- discussion topicBLG model
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active 3 days ago

Some comments at BLG model in the section “3-algebras” on a confusion of terms.

- Discussion Type
- discussion topicstrict 2-group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 3 days ago

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 topiccrossed module
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 15
- Last comment by Urs
- Last Active 3 days ago

At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group $\pi_2(X,A)$ together with the bundary map $\delta:\pi_2(X,A)\to \pi_1(A)$ and the $\pi_1(A)$-action on $\pi_2(X,A)$. As someone confirms this example is correct I’ll add it to crossed module.

- Discussion Type
- discussion topicFinSet
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by DavidRoberts
- Last Active 3 days ago

I have briefly recorded the equivalence of FinSet${}^{op}$ with finite Booplean algebras at

*FinSet – Properties – Opposite category*. Then I linked to this from various related entries, such as*finite set*,*power set*,*Stone duality*,*opposite category*.(I thought we long had that information on the $n$Lab, but it seems we didn’t)

- Discussion Type
- discussion topicexponential ideal
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active 3 days ago

Noted that this follows from Day’s reflection theorem.

- Discussion Type
- discussion topicDay's reflection theorem
- Category Latest Changes
- Started by Todd_Trimble
- Comments 1
- Last comment by Todd_Trimble
- Last Active 3 days ago

- Discussion Type
- discussion topicRezk completion
- Category Latest Changes
- Started by nLab edit announcer
- Comments 12
- Last comment by Guest
- Last Active 4 days ago

- Discussion Type
- discussion topicrelational beta-module
- Category Latest Changes
- Started by Todd_Trimble
- Comments 9
- Last comment by Guest
- Last Active 4 days ago

I’ve been adding a considerable amount of detail to relational beta-module. Not quite finished, but a lot of former ellipses have been filled in, and technical results proved from scratch.

If anyone knows this material, I’d enjoy hearing of any proposed simplifications. My local university library does not have the Springer Lecture Notes where Barr first wrote his article on relational beta-modules, and it’s hard finding detailed material at this ground level on the internet, so this represents pretty much what I’ve been able to work out by myself. (And it might read that way.)

- Discussion Type
- discussion topictopological space
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Guest
- Last Active 4 days ago

I tried to prettify the entry

*topological space*a bit more:made an attempt at adding an Idea-section (feel free to work on that, it’s just a quick idea motivated more from the desire to have such a section at all than from an attempt to do it any justice).

collected the three Definition-sections to subsections of a single Definition-section

polished and expanded the Standard definition section.