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created a reference-entry Homotopy Limit Functors on Model Categories and Homotopical Categories and added pointers to it to a bunch of relevant entries
In the term elimination row of the table in section 2, it seems to be taking as a variable under the bar. It should be the application of to an element judged to be in , no? As we have it in section 3.
added pointer to this video talk
which I just happened upon from André’s webpage. Apart from the content, this is performed quite remarkably.
In the abstract definition, in the 2nd paragraph about the -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.
some bare minimum at cut rule
added pointer to yesterday’s
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 of the category of presheaves
it should have
the equivalence classes of left exact reflective and accessivley embedded subcategories 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 of the category of presheaves
No?
(This is just a question. I didn’t make an edit. Yet.)
I added the reference
I have started a stub on this. (Isn’t there a nice nPOV interpretation of this?)
created a brief entry IKKT matrix model to record some references. Cross-linked with string field theory, and with BFSS matrix model
added pointer to:
I made “constructive logic” redirect to here (“constructive mathematics”) instead of to “intuitionistic mathematics”, as it used to
See also the discussion here.
added at cobordism hypothesis a pointer to
where the case for -categories is spelled out and proven in detail.
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.
added to homotopy fixed point a discussion of how the traditional ad-hoc formula that one finds in much of the literature (namely ) follows form first principles.
(This is for completeness, not because it is a big deal.)
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 as a morphism between objects and in a monoidal category as in categorical semantics, the Geometry of Interaction interprets it as an endomorphism on the object . 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).
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.
After looking at Russell’s paradox, one thing led to another and I wound up writing fixed-point combinator.
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.
for completeness, to go with U(ℋ), for the moment mainly in order to record references, such as:
recorded two references to physics application at exotic smooth structure
(no time for anything else)
added a bit more text to the Idea-section at Wick rotation and in particular added cross-links with Osterwalder-Schrader theorem.
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.
stub for jet bundle
brief category:people-entry for hyperlinking references at torsion theory
Linking to the new page torsion points of an elliptic curve.
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 (which is reasonable), but it then proceeds to give the external formulation of AC for such a , which I think is usually not the best meaning of “AC relative to ”. 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.
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)
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