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- Discussion Type
- discussion topicgraded algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2021

added pointer to:

- Gregory Karpilovsky, Chapter 2 of:
*The Algebraic Structure of Crossed Products*, Mathematics Studies**142**, North Holland 1987 (ISBN:9780080872537)

- Gregory Karpilovsky, Chapter 2 of:

- Discussion Type
- discussion topicderivation on a group
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Urs
- Last Active Aug 30th 2021

- Discussion Type
- discussion topicEric J. Moore
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2021

brief

`category:people`

-entry for hyperlinking references at*strict (2,1)-category*

- Discussion Type
- discussion topicPeter H. H. Fantham
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2021

brief

`category:people`

-entry for hyperlinking references at*strict (2,1)-category*

- Discussion Type
- discussion topicJosef Leutgeb
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2021

brief

`category:people`

-entry for hyperlinking references at*holographic QCD*and*anomalous magnetic moment*

- Discussion Type
- discussion topicAnton Rebhan
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2021

brief

`category:people`

-entry for hyperlinking references at*holographic QCD*and*anomalous magnetic moment*

- Discussion Type
- discussion topicanomalous magnetic moment
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by Urs
- Last Active Aug 30th 2021

there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).

I have added a remark on this in the $(g-2)$-entry here and also at

*quantum gravity*here.

- Discussion Type
- discussion topiclarge 1/N limit
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Aug 30th 2021

- Discussion Type
- discussion topicproduct of simplices
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Tim_Porter
- Last Active Aug 30th 2021

added pointer to:

- Greg Friedman, Section 5 of:
*An elementary illustrated introduction to simplicial sets*, Rocky Mountain J. Math. 42(2): 353-423 (2012) (arXiv:0809.4221, doi:10.1216/RMJ-2012-42-2-353)

- Greg Friedman, Section 5 of:

- Discussion Type
- discussion topiccovert space
- Category Latest Changes
- Started by Ulrik
- Comments 2
- Last comment by Urs
- Last Active Aug 29th 2021

- Discussion Type
- discussion topicgroupoid
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Aug 29th 2021

added to groupoid a section on the description in terms of 2-coskeletal Kan complexes.

- Discussion Type
- discussion topicweak equivalence of internal categories
- Category Latest Changes
- Started by DavidRoberts
- Comments 9
- Last comment by Urs
- Last Active Aug 29th 2021

Started weak equivalence of internal categories. Needs some more work, including examples and theorems.

- Discussion Type
- discussion topicstrict 2-limit
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 29th 2021

- Discussion Type
- discussion topicTomas Everaert
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by Tim_Porter
- Last Active Aug 29th 2021

- Discussion Type
- discussion topicPuppe exact category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active Aug 29th 2021

- Discussion Type
- discussion topiccanonical model structure
- Category Latest Changes
- Started by Richard Williamson
- Comments 2
- Last comment by Urs
- Last Active Aug 29th 2021

Linking to the page canonical model structure for 2-categories in a couple of places.

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 70
- Last comment by nLab edit announcer
- Last Active Aug 29th 2021

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 topicWhitehead product
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Tim_Porter
- Last Active Aug 29th 2021

- Discussion Type
- discussion topicexplicit substitution
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by valeriadepaiva
- Last Active Aug 28th 2021

- Discussion Type
- discussion topiccartesian closed category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Urs
- Last Active Aug 28th 2021

Added a subsection to cartesian closed category, the functional completeness theorem. (To be expanded upon, eventually.)

- Discussion Type
- discussion topicWhitehead theorem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Dmitri Pavlov
- Last Active Aug 28th 2021

created Whitehead theorem, including its (oo,1)-topos version

in that context I also created hypercomplete (infinity,1)-topos. maybe that should be merged eventually with hypercompletion.

- Discussion Type
- discussion topicEnrico Ghiorzi
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 28th 2021

brief

`category:people`

-entry for hyperlinking references at*internal category*

- Discussion Type
- discussion topicinternal category
- Category Latest Changes
- Started by Urs
- Comments 76
- Last comment by Urs
- Last Active Aug 28th 2021

I edited the formatting of internal category a bit and added a link to internal infinity-groupoid

it looks like the first query box discussion there has been resolved. Maybe we can remove that box now?

- Discussion Type
- discussion topicGrothendieck fibration
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active Aug 28th 2021

I made the former entry "fibered category" instead a redirect to Grothendieck fibration. It didn't contain any addition information and was just mixing up links. I also made category fibered in groupoids redirect to Grothendieck fibration

I also edited the "Idea"-section at Grothendieck fibration slightly.

That big query box there ought to be eventually removed, and the important information established in the discussion filled into a proper subsection in its own right.

- Discussion Type
- discussion topicGrothendieck construction
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Urs
- Last Active Aug 28th 2021

added to Grothendieck construction a section Adjoints to the Grothendieck construction

There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.

There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.

- Discussion Type
- discussion topicdouble category
- Category Latest Changes
- Started by John Baez
- Comments 16
- Last comment by Urs
- Last Active Aug 28th 2021

- 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 topiccartesian closed 2-category
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by Urs
- Last Active Aug 28th 2021

- Discussion Type
- discussion topiccombinatory logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 11
- Last comment by DavidRoberts
- Last Active Aug 28th 2021

I rescued combinatory logic from being a “my first slide” spam and gave it some content, mainly to record the fact (which I just learned) that under propositions as types, combinatory logic corresponds to a Hilbert system.

I feel like there should be something semantic to say here too, like $\lambda$-calculus corresponding to a “closed, unital, cartesian multicategory” (a cartesian multicategory that is “closed and unital” as in the second example here) and combinatory logic corresponding to a closed category that is also “cartesian” in some sense. Has anyone defined such a sense?

Relatedly, is there a notion of “linear combinatory logic” that would correspond to ordinary (symmetric) closed categories? My best guess is that instead of $S$ and $K$ you would have combinators with the following types:

$(B\to C) \to (A\to B) \to (A\to C)$ $(A \to (B\to C)) \to B \to A\to C$coming from the two ways to eliminate a dependency in $S$ to make it linear ($K$ is irreducibly nonlinear). These are of course the ways that you express composition and symmetry in a closed category.

- Discussion Type
- discussion topicempty 208
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active Aug 28th 2021

As i have obtained everything from MYSELF AS IM THE GLOBAL SOLO DADABASE ACROSS the world being taken away from me AND HES ON A MISSION AND I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with my current situation and I am not sure what to do with

Anonymous

- Discussion Type
- discussion topicFGA explained
- Category Latest Changes
- Started by DavidRoberts
- Comments 3
- Last comment by valeriadepaiva
- Last Active Aug 27th 2021

I updated a link on FGA explained to one of the chapters, to point to the arXiv version (the one on constructing Hilbert and Quot schemes). I also added a link to the conference page itself, which has links to scans of lecture notes, as the direct lecture notes links seem to be broken.

- Discussion Type
- discussion topicJimmie Lawson
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by valeriadepaiva
- Last Active Aug 27th 2021

brief

`category:people`

-entry for hyperlinking references at*convenient category of topological spaces*and*compactly generated topological spaces*

- Discussion Type
- discussion topicMarta Bunge
- Category Latest Changes
- Started by Tobias Fritz
- Comments 1
- Last comment by Tobias Fritz
- Last Active Aug 27th 2021

- Discussion Type
- discussion topicAlexandre Deur
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2021

brief

`category:people`

page for hyperlinking references at*QCD*and*hadron supersymmetry*

- Discussion Type
- discussion topicHarry J. Lipkin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2021

brief

`category:people`

-entry for hyperlinking references at*exotic hadron*and*hadron supersymmetry*

- Discussion Type
- discussion topichadron supersymmetry
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Aug 27th 2021

- Discussion Type
- discussion topicdiquark
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Aug 27th 2021

- Discussion Type
- discussion topicelementary (infinity,1)-topos
- Category Latest Changes
- Started by David_Corfield
- Comments 88
- Last comment by Mike Shulman
- Last Active Aug 27th 2021

I added the reference

- Nima Rasekh,
*A Theory of Elementary Higher Toposes*, (arXiv:1805.03805)

- Nima Rasekh,

- Discussion Type
- discussion topicanafunctor
- Category Latest Changes
- Started by DavidRoberts
- Comments 5
- Last comment by nLab edit announcer
- Last Active Aug 27th 2021

- Discussion Type
- discussion topicMax Guillen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2021

- Discussion Type
- discussion topicD=10 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2021

added pointer to today’s:

- Maor Ben-Shahar, Max Guillen,
*10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action*(arXiv:2108.11708)

- Maor Ben-Shahar, Max Guillen,

- Discussion Type
- discussion topicPaolo Gregori
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 27th 2021

brief

`category:people`

-entry for hyperlinking references at*SYK model*,*AdS2-CFT1 duality*and*resurgence*

- Discussion Type
- discussion topico-minimal structure
- Category Latest Changes
- Started by Todd_Trimble
- Comments 6
- Last comment by David_Corfield
- Last Active Aug 27th 2021

I started some short articles on o-minimal structure and structure (model theory).

- Discussion Type
- discussion topicconstructive mathematics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 27th 2021

I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to

- Discussion Type
- discussion topicLie algebroid
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Aug 26th 2021

Added:

A bijective correspondence between Lie algebroid structures, homological vector fields of degree 1, and odd linear Poisson structures is established in the paper

- A. Yu. Vaintrob,
*Lie algebroids and homological vector fields*, Russian Mathematical Surveys 52:2 (1997), 428–429. doi, vaintrob-lie-algebroids-and-homological-vector-fields.pdf:file.

- A. Yu. Vaintrob,

- Discussion Type
- discussion topicstrong epimorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 26th 2021

added pointer to:

- Francis Borceux, Def. 4.3.5 in:
*Handbook of Categorical Algebra*Vol. 1:*Basic Category Theory*, Encyclopedia of Mathematics and its Applications**50**Cambridge University Press (1994) (doi:10.1017/CBO9780511525858)

- Francis Borceux, Def. 4.3.5 in:

- Discussion Type
- discussion topicextremal epimorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 26th 2021

added pointer to:

- Francis Borceux, Def. 4.3.2 in:
*Handbook of Categorical Algebra*Vol. 1:*Basic Category Theory*, Encyclopedia of Mathematics and its Applications**50**Cambridge University Press (1994) (doi:10.1017/CBO9780511525858)

- Francis Borceux, Def. 4.3.2 in:

- Discussion Type
- discussion topicregular epimorphism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 26th 2021

added pointer to:

- Jiří Adámek, Horst Herrlich, George Strecker, Def. 7.71 in:
*Abstract and Concrete Categories – The Joy of Cats*John Wiley and Sons, New York (1990) reprinted as: Reprints in Theory and Applications of Categories**17**(2006) 1-507 (tac:tr17, book webpage, pdf)

- Jiří Adámek, Horst Herrlich, George Strecker, Def. 7.71 in:

- Discussion Type
- discussion topiceffective monomorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 26th 2021

added pointer to:

- Discussion Type
- discussion topicCynthia Lester
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 26th 2021

brief

`category:people`

-entry for hyperlinking references at*canonical Grothendieck topology*

- Discussion Type
- discussion topiccanonical topology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 26th 2021

somebody asked me for the proof of the claim at

*canonical topology*that for a Grothendieck topos $\mathbf{H}$ we have $\mathbf{H} \simeq Sh_{can}(\mathbf{H})$.I have added to the entry pointers to the proof in Johnstone’s book, and to related discussion for $\infty$-toposes. Myself I don’t have more time right now, but maybe somebody feels inspired to write out some details in the nLab entry itself?

- Discussion Type
- discussion topicpseudo-torsor
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Aug 26th 2021

for completeness, with pointer to

- Alexander Grothendieck et al., 16.5.15 in:
*Éléments de géométrie algébrique*IV_4. Étude locale des schémas et des morphismes de schémas (Quatrième partie) Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361. Ch.IV.§16–21 (numdam:PMIHES_1967__32__5_0)

- Alexander Grothendieck et al., 16.5.15 in:

- Discussion Type
- discussion topicchaos
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 25th 2021

a stub, for the moment just so as to give a home to

- William Lawvere,
*Functional Remarks on the General Concept of Chaos*, IMA reprint 87, 1984 (pdf)

- William Lawvere,

- Discussion Type
- discussion topicdiscrete and indiscrete topology
- Category Latest Changes
- Started by Urs
- Comments 31
- Last comment by Urs
- Last Active Aug 25th 2021

created discrete and codiscrete topology

- Discussion Type
- discussion topiccodiscrete groupoid
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 25th 2021

- Discussion Type
- discussion topicreflective sub-(infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 25th 2021

Where it said, unhelpfully:

You can read this as the evident characterization of adjoints…

I have now expanded to:

You may read this as the characterization of adjoint functors via universal arrows (via this prop.)…

- Discussion Type
- discussion topicflavors of higher toposes -- list
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 25th 2021

- Discussion Type
- discussion topic1-topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 25th 2021

added cross-links of this ancient entry with

*higher topos theory*and with*2-topos*etc.Notice that there is an old unresolved discussion box here.

- Discussion Type
- discussion topic(1,2)-topos
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Urs
- Last Active Aug 25th 2021

- Discussion Type
- discussion topicL-finite category
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Mike Shulman
- Last Active Aug 25th 2021

added pointer (below a new Proposition-environment here) to where Paré states/proves the characterizations of L-finite limits (namely on his p. 740, specifically in his Prop. 7 – this also makes clear which typo the footnote is about).

Similarly I added pointer (below a new Remark-environment here) to where Paré discusses the relation to K-finitness (namely the next page), together with attribution to Richard Wood.

- Discussion Type
- discussion topichigher topos theory
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Mike Shulman
- Last Active Aug 25th 2021