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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
For the sake of illustration I have added to ordinary homology a section In terms of higher linear algebra.
Currently the main point is to record, after some preliminaries, the standard observation plus detailed proof that for X a topological space, its ordinary chain complex of singular simplices is, up to equivalence, the ∞-colimit of the tensor unit local system with coefficients in HkMod. (Its “Hk-Thom spectrum”.)
In the section compacta as algebras, I have written out complete details of a proof that compact Hausdorff spaces are monadic over sets.
concerning stable map: is there some nice abstract characterization? Something involving maybe the words “faithful functor of étale groupoids”?
Added a section with a little bit of detail on model structures on cochain complexes in non-negative degree to model structure on chain complexes.
localizer, just for completeness
created a minimum at Hermitian structure.
Also edited and expanded the Idea- section at Käher structure a bit.
stub for compact closed 2-category to accomodate a pointer to Mike Stay’s recent article
I am starting an entry Poincaré duality algebra, but it still needs some attention
created unitisation of C*-algebras
stub for chiral ring
(not good yet)
I began to expand Tarski-Seidenberg theorem (formerly a stub) by including some commentary on its significance, and some related results. This is to help create a niche for Schanuel’s conjecture, yet to be written, but which was invoked in a discussion at MO.
stub for metaplectic correction
brief statement of Kodaira vanishing theorem for the complex geometry case
started a stub equivariant KK-theory with some quick notes. But still very stubby.
Wrote a section General weighted colimit formula at homotopy colimit
giving a general formula
spelling out the special case of simplicial diagrams, that reproduces the Bousfield-Kan formula
spelling out the special case of pushout diagrams, that reproduces the formula (or its dual) discussed more in detail in the other examples that were already present
I tried to collect some references at crossed product C*-algebra on their relation to convolution C*-algebras of action groupoids. But I guess I run out of steam…
while writing Baum-Connes conjecture I happened to add some stuff to analytic assembly map.
I have added a new paragraph to direct image about direct image functor with compact support f!F. Eventually I would create a separate entry direct image with compact support, but not yet.
started dual morphism but then began to hesitate: we must have this discussion somewhere already. But where?
Treating locally path-connected spaces as nice topological spaces, we see that nice path-connected spaces are the same as nice connected spaces, and the definition of the latter is more elementary (in point-set topology) than the former. Then nice simply connected spaces are the same as nice unicoherent spaces, which are again more elementary. This should continue for the entire hierarchy of n-connected spaces, so I wrote something there about it.
started a table of contents integration theory - contents and added it as a floating TOC to the relevant entries.
(Mostly as a reminder to myself to write more on fiber integration in generalized cohomology…)
Added the following to the references at stable homotopy theory and algebraic topology:
Brief indications of open questions and future directions (as of 2013) of algebraic topology and stable homotopy theory are in
- Tyler Lawson, The future, Talbot lectures 2013 (pdf)
created asymptotic series
Someone started a page called probability amplitudes but with a single word. I have changed that to say the page is empty. (which of course it is not!) as I did not feel competent to write even a stub on that topic.
created models in presheaf toposes with the statement of the fact that T-models in presheaves are presheaves of T-models, at least for T a geometric theory.
Added a pointer to this from the corresponding discussion at group object.
I made a stub uniform convergence space, but I need to read the reference.
created a table holographic principle – table (meant to show at on glance what the dictionaty is) and included it into the relevant entries.
stub for perfect complex
I have added to Knizhnik-Zamolodchikov connection
a new paragraph in the Idea section: Idea – From geometric quantization of Chern-Simons theory
a bunch of commented references
There was some misnumbering (sometimes off by 1, sometimes reversed) at homotopy group#truncconn, which hopefully I've fixed.
added to odd line a brief remark on the nature of its automorphism super-group and the consequences, also added some relevant references.
(I feel like I had added this statement to the nLab elsewhere already long time ago, but can’t find it now.)
I was fixing some Spam at generator and noticed that Grothendieck category has a link to generator, but shouldn’t this be to separator? I have fixed it so that the term generator in Grothendieck category links to separator.
I tried to clear up some formatting problems / typos at separator. (There is a query near the bottom of the page that seems to still be unanswered.) Can someone glance at the entry to check my reformatting is right as I was on autopilot when doing it!
A short note at denial inequality, since the subject came up. Mike, please check that I used ‘disequality’ correctly.
Just now I needed a definition and discussion of term algebra for the new entry on Lindenbaum-Tarski algebra. I noted we have Lindenbaum algebra in several places with no explanation. I am no logician and have very few logic books available. Are these the same and what generality should be used for the term algebra.
I also looked at the entry on Boolean algebra and was a bit surprised to find there was no elementary algebraic version given. This is the (for dummies) version perhaps, but seeing one of the usual algebraic description and examples (although these are in the Wikipedia page I’m sure) might enable the ideas about Heyting algebras, lattices, etc., there to be more useful. I’m not sure what level to pitch any additions to that entry, any ideas or thoughts anyone?
Just a stub at logical connective.
I am going to rewrite a part of the Baer sum, the section “On short exact sequences”, partly following S. MacLane, Homology, 1963 (he does the version for extensions of R-modules). I am not fully understanding and would like to discuss the issue, but I think the current notation is a bit hiding. So here is the version of the section before my update, so it can be reversed if somebody not happy:
For 0→A→ˆGi→G→0 for i=1,2 two short exact sequences of abelian groups, their Baer sum is
ˆG1+ˆG2≔+*Δ*ˆG1׈G2The first step forms the pullback of the short exact sequence along rhe diagonal on G:
A⊕A→A⊕A↓↓Δ*(ˆG1⊕ˆG2)→ˆG1⊕ˆG2↓↓GΔG→G⊕GThe second forms the pushout along the addition map on A:
A⊕A+→A↓↓Δ*(ˆG1⊕ˆG2)→+*Δ*(ˆG1⊕ˆG2)↓↓G→GI’ve changed Postnikov system definition 2
the part saying
“The map X→imn(f) induces an epimorphism on connected components”
to
“The map X→imn(f) induces an epimorphism on homotopy groups in degree n−1”.
This was a small issue that confused me.
There is a query at axiom K.
added a pointer to the old lecture
to GUT and string phenomenology .
earlier today I had started splitting off entries intensional type theory and extensional type theory from type theory. But then the Lab halted and now it’s left in somewhat stubby form.
I've seen two meanings for this term, and they are both at limit point, along with a family of other terms for various arity classes.
Urs created limit of a sequence on this topic.
I have finally split off super line 2-bundle to a stand-alone entry (it used to be a subsection at line 2-bundle).
I discovered via MO that we have an entry hereditarily finite set, which was a bit lonesome. So I have now tried to cross-link it a bit with related entries.
In particular at finite object in “Related entries” I started a list with related entries – probably incomplete, please expand. In the course of this I created als a brief entry finite (infinity,1)-category by splitting off a paragraph form finite (infinity,1)-limit.
I saw that one of the classical arity classes didn't have a name, so I named it ‘subunary’.
last Friday, when the nForum was down, I had created very brief entries
and
I just deleted the query
Did you do these edits attributed to ’Ronald null Brown’? —Toby
at Ronnie Brown.
A bit of classical stuff at semicontinuous map.
started a stub for the B-model
stub for integral Morava K-theory
created Diaconescu-Moore-Witten anomaly, so far just with a bunch of (briefly commented) references
put the bare minimum definition into height of a formal group
A few grad students and I are starting a reading group on the Firewall problem and related aspects, so I’ve created a page in the nLab with a bunch of relevant papers:
(not yet a complete list.)
The goal will be to develop the page into a introduction to the problem, and the resolutions proposed, etc.
I have created a table
and included it into the relevant entries.
It looks like this:
| geometric context | universal additive bivariant (preserves split exact sequences ) | universal localizing bivariant (preserves all exact sequences) | universal additive invariant | universal localizing invariant |
|---|---|---|---|---|
| noncommutative algebraic geometry | noncommutative motives Motadd | noncommutative motives Motloc | algebraic K-theory | non-connective algebraic K-theory |
| noncommutative topology | KK-theory | E-theory | operator K-theory | … |
I am not sure what should go in the bottom right corner.
stub for non-connective algebraic K-theory
you all knew it was about to happen, and now it did: I have created a table-of-contents page for inclusion as “floating TOC” in the relevant entries:
added to limit in a quasi-category (in the Properties-section) more details on how the definition in terms of over over-categories is equivalent to the one in terms of homs. But still not done.