# Start a new discussion

## Not signed in

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

## Site Tag Cloud

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

• 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.

• Corrected elimination rule.

• added pointer to this video talk

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

• Created.

• Added remark on geometric realizations of pairs of adjoint functors

Roman T

• 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.

• Page created, but author did not leave any comments.

Anonymous

• Ooops, failed to use my full name during edit!

Linas Vepstas

• am finally giving $\overline{W}G$ its own entry, for ease of hyperlinking to it

• 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.
• typo

Tim Richter

• 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 of

the 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 presheaves

Or 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 presheaves

No?

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

• updated link to my webpage

• I added the reference

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

• brief category:people-entry for hyperlinking references

• polished layout, added example of $2I$

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• added the statement that monos are preserved by homotopy pushout.

• brief category:people-entry for hyperlinking references

• 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.

• I added some more detail on the p-torsion of a group scheme

Hari Rau-Murthy

• starting an entry, for the moment mainly in order to record the fact that “crossed homomorphisms” are equivalently homomorphic sections of the corresponding semidirect product group projection. This is obvious, but is there a reference that makes it explicit?

• 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.)

• changed page name to singular

• 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?

• Finally splitting this off from lattice QCD in order to record some references. Gave it a rough Idea-section, but this remains a stub.

• 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.

• I have tried my hand at an illustration: here

• Page created, but author did not leave any comments.

• added a bare minimum on $(p,q)$5-brane webs.

• I added a couple more references to Bayesian reasoning used in physics.

• starting something, not done yet

• 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.

• fixing typo

Anonymous

• brief category:people-entry for hyperlinking references at torsion theory

• starting a collection of commented references here. This is to be !include-ed in the References-section of related entries. Therefore this entry starts out with a sub-section and contains nothing else.

• 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.)

• 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

Will be adding more as I find more.

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

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.