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- Discussion Type
- discussion topicHomotopy Limit Functors on Model Categories and Homotopical Categories
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Dec 19th 2021

created a reference-entry Homotopy Limit Functors on Model Categories and Homotopical Categories and added pointers to it to a bunch of relevant entries

- Discussion Type
- discussion topicdependent product type
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by varkor
- Last Active Dec 19th 2021

In the term elimination row of the table in section 2, it seems to be taking $x: X$ as a variable under the bar. It should be the application of $f$ to an element judged to be in $X$, no? As we have it in section 3.

- Discussion Type
- discussion topicdependent product natural deduction - table
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Dec 19th 2021

- Discussion Type
- discussion topic(infinity,n)-category of cobordisms
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 19th 2021

added pointer to this video talk

- André Henriques,
*The complex cobordism 2-category*, 2021 (video)

which I just happened upon from André’s webpage. Apart from the content, this is performed quite remarkably.

- André Henriques,

- Discussion Type
- discussion topicBernardo Uribe
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 19th 2021

- Discussion Type
- discussion topicHigher categories and homotopical algebra
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Urs
- Last Active Dec 19th 2021

- Discussion Type
- discussion topicgeometric realization of categories
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Dec 18th 2021

- Discussion Type
- discussion topicdirected limit
- Category Latest Changes
- Started by jesuslop
- Comments 1
- Last comment by jesuslop
- Last Active Dec 18th 2021

In the abstract definition, in the 2nd paragraph about the $\kappa$-directed version, I’d say It looks that the bound should be “lower” instead of “upper”, so the direction in the first two paragraphs both go downward.

- Discussion Type
- discussion topicmutations of exceptional collections
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by David_Corfield
- Last Active Dec 18th 2021

- Discussion Type
- discussion topicempty 211
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active Dec 17th 2021

- Discussion Type
- discussion topiccut rule
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by nLab edit announcer
- Last Active Dec 17th 2021

some bare minimum at

*cut rule*

- Discussion Type
- discussion topicsimplicial classifying space
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Tim_Porter
- Last Active Dec 17th 2021

- Discussion Type
- discussion topiclocally presentable category
- Category Latest Changes
- Started by Tobias Fritz
- Comments 11
- Last comment by varkor
- Last Active Dec 17th 2021

- In the definition, the article states "every object in C is a small object (which follows from 2 and 3)". The bracketed remark doesn't seem quite right to me, since neither 2 nor 3 talk about smallness of objects. Presumably this should better be phrased as in A.1.1 of HTT, "assuming 3, this is equivalent to the assertion that every object in S is small".

Am I right? I don't (yet) feel confident enough with my category theory to change this single-handedly.

- Discussion Type
- discussion topichistorical note on characteristic classes
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Dec 17th 2021

- Discussion Type
- discussion topicinfrared divergence
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 16th 2021

added pointer to yesterday’s

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

- Paweł Duch,

- Discussion Type
- discussion topicsheaf toposes are equivalently the left exact reflective subcategories of presheaf toposes
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Dec 16th 2021

It’s still not quite right, is it? (here) After

Moreover, up to equivalence, every Grothendieck topos arises this way:

isn’t there the clause of

*accessible*embedding missing? I.e. instead ofthe equivalence classes of left exact reflective subcategories $\mathcal{E} \hookrightarrow PSh(\mathcal{C})$ of the category of presheaves

it should have

the equivalence classes of left exact reflective

**and accessivley embedded**subcategories $\mathcal{E} \hookrightarrow PSh(\mathcal{C})$ of the category of presheavesOr else, by the prop that follows, it should say

the equivalence classes of left exact reflective

**and locally presentable**subcategories $\mathcal{E} \hookrightarrow PSh(\mathcal{C})$ of the category of presheavesNo?

(This is just a question. I didn’t make an edit. Yet.)

- Discussion Type
- discussion topicMarc Hoyois
- Category Latest Changes
- Started by Marc Hoyois
- Comments 1
- Last comment by Marc Hoyois
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicelementary (infinity,1)-topos
- Category Latest Changes
- Started by David_Corfield
- Comments 89
- Last comment by Urs
- Last Active Dec 16th 2021

I added the reference

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

- Nima Rasekh,

- Discussion Type
- discussion topicQuillen plus construction
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Dec 16th 2021

I have started a stub on this. (Isn’t there a nice nPOV interpretation of this?)

- Discussion Type
- discussion topicYuhma Asano
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicIKKT matrix model
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Dec 16th 2021

created a brief entry

*IKKT matrix model*to record some references. Cross-linked with*string field theory*, and with*BFSS matrix model*

- Discussion Type
- discussion topicperfect group
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Tim_Porter
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicHajime Ishihara
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicreverse mathematics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2021

added pointer to:

- Hannes Diener,
*Constructive Reverse Mathematics*, 2018 (arXiv:1804.05495, dspace:ubsi/1306)

- Hannes Diener,

- Discussion Type
- discussion topicHannes Diener
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicconstructive mathematics
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 16th 2021

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

- Discussion Type
- discussion topicMichael J. Beeson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 16th 2021

- Discussion Type
- discussion topicepimorphism in an (infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Dec 15th 2021

See also the discussion here.

- Discussion Type
- discussion topiccobordism hypothesis
- Category Latest Changes
- Started by Urs
- Comments 55
- Last comment by Urs
- Last Active Dec 15th 2021

added at cobordism hypothesis a pointer to

- Yonatan Harpaz,
*The Cobordism Hypothesis in Dimension 1*(arXiv:1210.0229)

where the case for $(\infty,1)$-categories is spelled out and proven in detail.

- Yonatan Harpaz,

- Discussion Type
- discussion topicmonomorphism in an (infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Dec 15th 2021

- Discussion Type
- discussion topicJoseph-Louis Lagrange
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 15th 2021

- Discussion Type
- discussion topicLagrange's theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 15th 2021

The term “Lagrange’s theorem” used to redirect to

*index of a subgroup*, where it is mentioned only towards the end. So I am giving it its own little entry now.

- Discussion Type
- discussion topicp-torsion
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by Richard Williamson
- Last Active Dec 15th 2021

- Discussion Type
- discussion topiccrossed homomorphism
- Category Latest Changes
- Started by Urs
- Comments 36
- Last comment by Urs
- Last Active Dec 15th 2021

- Discussion Type
- discussion topichomotopy fixed point
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 15th 2021

added to

*homotopy fixed point*a discussion of how the traditional ad-hoc formula that one finds in much of the literature (namely $X^{h G} = Hom_G(E G, X)$) follows form first principles.(This is for completeness, not because it is a big deal.)

- Discussion Type
- discussion topicgroup actions on spheres
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by Urs
- Last Active Dec 15th 2021

- Discussion Type
- discussion topicGeometry of Interaction
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by nLab edit announcer
- Last Active Dec 15th 2021

David C. has kindly created a list of references at

*Geometry of Interaction*. I have now started there an Idea section:What has been called

*Geometry of Interaction*(Girard 89) is a kind of semantics for linear logic/linear type theory that is however different in method from the usual categorical semantics in monoidal categories. Instead of interpreting a proof of linear implication $A\multimap B$ as a morphism between objects $A$ and $B$ in a monoidal category as in categorical semantics, the*Geometry of Interaction*interprets it as an endomorphism on the object $A\multimap B$. This has been named*operational semantics*to contrast with the traditional*denotational semantics*.That also the “operational semantics” of GoI has an interpretation in category theory, though, namely in traced monoidal categories was first suggested in (Joyal-Street-Verity 96) and then developed out in (Haghverdi 00, Abramsky-Haghverdi-Scott 02,Haghverdi-Scott 05).

- Discussion Type
- discussion topiclift
- Category Latest Changes
- Started by David_Corfield
- Comments 14
- Last comment by Richard Williamson
- Last Active Dec 15th 2021

Started lift.

weak factorization system has redirects from: lifting property, right lifting property, left lifting property, lifting problem, lifting problems.

Would it be better to have these redirect to lift?

- Discussion Type
- discussion topicsign problem in lattice QCD
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 14th 2021

Finally splitting this off from

*lattice QCD*in order to record some references. Gave it a rough Idea-section, but this remains a stub.

- Discussion Type
- discussion topicfixed-point combinator
- Category Latest Changes
- Started by Todd_Trimble
- Comments 25
- Last comment by DavidRoberts
- Last Active Dec 13th 2021

After looking at Russell’s paradox, one thing led to another and I wound up writing fixed-point combinator.

- Discussion Type
- discussion topicpartial combinatory algebra
- Category Latest Changes
- Started by Todd_Trimble
- Comments 8
- Last comment by joseville
- Last Active Dec 13th 2021

I have been adding material to partial combinatory algebra.

I plan on linking this to an article on functional completeness for cartesian closed categories, and on deduction theorems for various simple calculi.

- Discussion Type
- discussion topictautological line bundle
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Dec 13th 2021

- Discussion Type
- discussion topicreductive Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Dec 13th 2021

- Discussion Type
- discussion topicPU(ℋ)
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Dec 13th 2021

for completeness, to go with

*U(ℋ)*, for the moment mainly in order to record references, such as:- David John Simms,
*Topological aspects of the projective unitary group*, Math. Proc. Camb. Phil. Soc.**68**1 (1970) 57-60 (doi:10.1017/S0305004100001043)

- David John Simms,

- Discussion Type
- discussion topicsoft graviton theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 13th 2021

- Discussion Type
- discussion topic(p,q)5-brane
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Dec 12th 2021

- Discussion Type
- discussion topicBayesian reasoning
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by David_Corfield
- Last Active Dec 12th 2021

- Discussion Type
- discussion topicMay recognition theorem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Hurkyl
- Last Active Dec 10th 2021

- Discussion Type
- discussion topicexotic smooth structure
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by David_Corfield
- Last Active Dec 10th 2021

recorded two references to physics application at exotic smooth structure

(no time for anything else)

- Discussion Type
- discussion topicWick rotation
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Dec 10th 2021

added a bit more text to the Idea-section at

*Wick rotation*and in particular added cross-links with*Osterwalder-Schrader theorem*.

- Discussion Type
- discussion topicformal concept analysis
- Category Latest Changes
- Started by Tim_Porter
- Comments 18
- Last comment by Tim_Porter
- Last Active Dec 9th 2021

I have created formal concept analysis, as a place to put material from the Café discussions, but also to develop some of the concepts a bit further.

- Discussion Type
- discussion topicChu spaces, simple examples
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Tim_Porter
- Last Active Dec 9th 2021

- Discussion Type
- discussion topicjet bundle
- Category Latest Changes
- Started by Urs
- Comments 60
- Last comment by nLab edit announcer
- Last Active Dec 8th 2021

stub for jet bundle

- Discussion Type
- discussion topicSpencer Ernst Dickson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 8th 2021

brief

`category:people`

-entry for hyperlinking references at*torsion theory*

- Discussion Type
- discussion topictorsion subgroup
- Category Latest Changes
- Started by Richard Williamson
- Comments 3
- Last comment by Urs
- Last Active Dec 8th 2021

Linking to the new page torsion points of an elliptic curve.

- Discussion Type
- discussion topicweight systems on chord diagrams in physics
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Dec 7th 2021

- Discussion Type
- discussion topicaxiom of choice
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by jesuslop
- Last Active Dec 7th 2021

I’m not entirely happy with the introduction (“Statement”) to the page axiom of choice. On the one hand, it implies that the axiom of choice is something to be considered relative to a given category $C$ (which is reasonable), but it then proceeds to give the

*external*formulation of AC for such a $C$, which I think is usually not the best meaning of “AC relative to $C$”. I would prefer to give the Statement as “every surjection in the category of sets splits” and then discuss later that analogous statements for other categories (including both internal and external ones) can also be called “axioms of choice” — but with emphasis on the internal ones, since they are what correspond to the original axiom of choice (for sets) in the internal logic.(I would also prefer to change “epimorphism” for “surjection” or “regular/effective epimorphism”, especially when generalizing away from sets.)

- Discussion Type
- discussion topicexotic 7-sphere
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Dec 7th 2021

am splitting off this entry from

*exotic smooth strcuture*, in order to facilitate linking to specifically the case of exotic 7-sphere.Accordingly, so far the bulk of the entry is just copied over from the corresponding section at

*exotic smooth structure*,But I also added a new paragraph,

and that is what motivated me to split this off. Namely it occured to me that from the point of view of M-theory on 8-manifolds, Milnor’s classical construction of exotic smooth 7-spheres as boundaries of 8-manifolds is very particularly the construction of near horizon limits of black M2-brane spacetimes in the context of M-theory on 8-manifolds.

This must be known in the literature, and I’d like to collect what is known about it. So far I found a brief comment in this direction, in section 3.2 of

- David Morrison, M. Ronen Plesser, section 3.2 of
*Non-Spherical Horizons, I*, Adv.Theor.Math.Phys.3:1-81, 1999 (arXiv:hep-th/9810201)

Will be adding more as I find more.

- David Morrison, M. Ronen Plesser, section 3.2 of

- Discussion Type
- discussion topicSpin(11,3)
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by David_Corfield
- Last Active Dec 7th 2021

I am giving this group a stub entry just to have a decent place to record today’s

- Kirill Krasnov,
*$Spin(11,3)$, particles and octonions*(arXiv:2104.01786)

For this entry not to be all too lonely I made Spin(10,2) point to D=12 supergravity, for the moment. In the long run all this derserves to be expanded on, clearly.

- Kirill Krasnov,

- Discussion Type
- discussion topicAllen Hatcher
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Dec 7th 2021

Added a redirect from Alan Hatcher. (Incidentally, that page was made only a few months after the previous page of the same name was moved to Alan Hatcher > history)

Anonymous