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

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

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

• the book Monoidal Functors, Species and Hopf Algebras is very good, but still being written. Clearly the current link under which it is found on the web is not going to be the permanent link. So I thought it is a bad idea to link to it directly. Instead I created that page now which we can reference then from nLab entries. When the pdf link changes, we only need to adapt it at that single page.

• Where the page has

The index theorem is supposed to have an interpretation in terms of the quantum field theory of the superparticle on the given space,

is the “is supposed to” necessary? Why not “has an interpretation”? Is it just the general issue of any translation from mathematics to physics?

• Added how small categories can be thought of as semigroups.

• Did anyone ever write out on the $n$Lab the proof that for $X$ locally compact and Hausdorff, then $Map(X,Y)$ with the compact-open topology is an exponential object? (Many entries mention this, but I don’t find any that gets into details.)

I have tried to at least add a pointer in the entry to places where the proof is given. There is prop. 1.3.1 in

• Marcelo Aguilar, Samuel Gitler, Carlos Prieto, sections 1.2, 1.3 of Algebraic topology from a homotopical viewpoint, Springer (2002) (toc pdf)

but of course there are more canonical references. I also added pointer to

• Eva Lowen-Colebunders, Günther Richter, An Elementary Approach to Exponential Spaces, Applied Categorical Structures May 2001, Volume 9, Issue 3, pp 303-310 (publisher)
• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

• Chris Nagele, Oliver Janssen, Matthew Kleban, Decoherence: A Numerical Study (arXiv:2010.04803)
• Is the Strøm model category left proper? I know that pushout along cofibrations of homotopy equivalences of the form $A \to \ast$ are again homotopy equivalences. (e.g. Hatcher 0.17) Maybe the proof directly generalizes, haven’t checked.

• following a suggestion by Zoran, I have created a stub (nothing more) for Kuiper’s theorem

• am finally giving this its own entry. Nothing much here yet, though, still busy fixing some legacy cross-linking…

• started some remarks at physical unit. But I really need to stop with that now and do more urgent things…

• The entry used to start out with the line “not to be confused with neutral element”. This was rather suboptimal. I have removed that sentence and instead expanded the Idea-section to read now as follows:

Considering a ring $R$, then by the unit element one usually means the neutral element $1 \in R$ with respect to multiplication. This is the sense of “unit” in terms such as nonunital ring.

But more generally a unit element in a unital (!) ring is any element that has an inverse element under multiplication.

This concept generalizes beyond rings, and this is what is discussed in the following.

• brief category:people-entry for hyperlinking references

• At first Zoran's reply to my query at structured (infinity,1)-topos sounded as though he were saying "being idempotent-complete" were a structure on an (oo,1)-category rather than just a property of it. That had me worried for a while. It looks, though, like what he meant is that "being idempotent" is structure rather than a property, and that makes perfect sense. So I created idempotent complete (infinity,1)-category.

• brief category:people-entry for hyperlinking references

• am giving this its own entry, in order to record sufficient conditions on topological subgroup inclusions $H \subset G$ for the coset space coprodoction $G \to G/H$ to admit local sections.

So far I have two original references here (Gleason 50, Mostert 53). One should add some textbook account, too.

Am also referencing this at closed subgroup, at coset space and maybe elsewhere.

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

• am finally giving this its own page, and making “well-pointed topological group” etc. redirects to here.

Not done yet, but need to save.

• starting something

• brief category:people-entry for hyperlinking references

• added the statement (here) that every paracompact Banach manifold is an absolute neighbourhood retract

• splitting off this definition from neighborhood retract, for ease of linking, and in order to record the characterization AR = ANR+contractible

• Many additions and changes to Leibniz algebra. The purpose is to outline that the (co)homology and abelian and even nonabelian extensions of Leibniz algebras follow the same pattern as Lie algebras. One of the historical motivations was that the Lie algebra homology of matrices which lead Tsygan to the discovery of the (the parallel discovery by Connes was just a stroke of genius without an apparent calculational need) cyclic homology. Now, if one does the Leibniz homology instead then one is supposedly lead the same way toward the Leibniz homology (for me there are other motivations for Leibniz algebras, including the business of double derivations relevant for the study of integrable systems).

Matija and I have a proposal how to proceed toward candidates for Leibniz groups, that is an integration theory. But the proposal is going indirectly through an algebraic geometry of Lie algebras in Loday-Pirashvili category. Maybe Urs will come up with another path if it drags his interest.

• added references: Bolzano and Bolzano’s logic in the Stanford Encyclopedia of Philosophy

AnodyneHoward

• Gave this a dedicated page.

• Created.

• brief category:people-entry for hyperlinking references

• brief category:people-entry for hyperlinking references

Anonymous

• I edited stable (infinity,1)-category a bit:

* rephrased the intro part, trying to make it more forcefully to the point (not claiming to have found the optimum, though)

* added a dedicated section <a href="http://ncatlab.org/nlab/show/stable+(infinity%2C1)-category#the_homotopy_category_of_a_stable_category_triangulated_categories_7">The homotopy cat of a stable (oo,1)-cat: traingulated categories</a> to highlight the important statement here, which was previously a bit hidden in the main text.

• made some minor cosmetic edits, such as replacing

  \bar W G


(which comes out with too short an overline) with

  \overline{W} G

• a bare sub-section with a list of references – to be !included into relevant entries – mainly at confinement and at mass gap problem (where this list already used to live)

• at monadicity theorem in the second formulation of the theorem, item 3, it said

$C$ has

I think it must be

$D$ has

and have changed it accordingly. But have a look.

• I have expanded the Idea section at state on a star-algebra and added a bunch of references.

The entry used to be called “state on an operator algebra”, but I renamed it (keeping the redirect) because part of the whole point of the definition is that it makes sense without necessarily having represented the “abstract” star-algebra as a C*-algebra of linear operators.