Not signed in (Sign In)

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • Dedekind completions of quasiorders (not just linear orders) may now be found at Dedekind completion. Example: the lower Dedekind completion of the quasiorder of continuous functions is the quasiorder of lower semicontinuous functions.

    • I put a bunch of stuff there that might be of interest to the logicians and foundationalists among us, although it’s still pretty trivial.

    • Am I correct in supposing that the first definition of Dedekind cuts at real numbers object is missing an openness condition (as given in the later, power object-using definition on the same page)?
    • I have started a floating table of contents group theory - contents, and started adding it to some relevant entries

      (the toc is neither meant to already be complete nor to be optimally organized, please expand and polish as you see the need)

    • Another new article: sequence space. I await the inevitable report that this term is also used for other things.

    • New page: Banach coalgebra.

      Hopefully you all know that l 1l^1 is a Banach algebra under convolution, but did you know that l l^\infty is a Banach coalgebra under nvolution? (Actually, they are both Banach bialgebras!)

    • created a little table: chains and cochains - table and included it into the relevant entries (some of which still deserve to be edited quite a bit).

    • I have created a table relations - contents and added it as a floatic TOC to the relevant entries.

    • I added a few observations under a new section “Results” at bornological set. Bornological sets form a quasitopos. I don’t have a good reference for the theorem of Schanuel.

      Related is an observation which hadn’t occurred to me before: the category of sets equipped with a reflexive symmetric relation is a quasitopos. I’d like to return to this sometime in the context of thinking about morphisms of (simple) graphs.

    • I have started an entry (∞,n)-category with adjoints, prompted by wanting to record these slides:

      • Nick Rozenblyum, Manifolds, Higher Categories and Topological Field Theories, talk Northwestern University (2012) (pdf slides)

      If anyone can say more about the result indicated there, I’d be most grateful for a comment.

      Also, I seem to hear that at Luminy 2012 there was some extra talk, not appearing on the schedule (maybe by Nick Rozenblyum, but I am not sure) on something related to geometric quantization. If anyone has anything on that, I’d also be most grateful.

    • I am starting a table of contents, to be included as a floating TOC for entries related to duality:

      duality - contents

      But it’s a bit rough for the time being. I haven’t decided yet how to best organize it and I am probably still lacking many items that deserve to be included. To be developed. All input is welcome.

    • I started the article Z-infinity-module. Hopefully someone here can say something more interesting about them!

    • I'm putting all the big duality theorems from measure theory at Riesz representation theorem. Only a couple are filled in so far, but I'm out of time for today.

    • Heya. I haven’t actually made the necessary changes, but the various pages on dependent type theory make the statement that every DTT or MLTT is the internal logic of an LCCC and every LCCC is the categorical semantics of some DTT/MLTT. However, this is extremely confusing (it took me 2 or 3 hours to find a page where it was made completely clear), since it makes explicit use of super-strong extensionality (I think this is called beta-translation), that is to say, it is a theorem about extensional DTTs/MLTTs.

      It’s not even totally clear to me that every intensional type theory actually has an (∞,1)-categorical semantics without the consideration of the univalence axiom. I would make this clearer, but I am really out of my depth with type theories, so I’m just alerting you to the fact that this is stated confusingly almost everywhere (the only place where it’s clear is in the page on identity types).

    • Disambiguation: dual. Here I listed all of the pages on a kind of dual (but not a kind of duality, which is at duality).

    • New page: positive cone, including the extended positive cone of a W*-module.

    • Wrote Lambert W function. It was an excuse to record Joyal’s proof of Cayley’s theorem on the number of tree structures one can put on an nn-element set (which is n n2n^{n-2}).

    • I created a stub on excision, but this is just a link to the Wikipedia page for the moment.

    • Concrete, abstract: group actions, groups; concrete categories, categories; Cartesian spaces, vector spaces; von Neumann algebras, W *W^*-alebras; material sets, structural sets; etc. At concrete structure.

    • as some of you will have seen, I had spent part of the last week with attending talks at String-Math 2012 and posting some notes about these, to the nnCafé (here). For many of these notes I added material to existing nnLab entries (mostly just references) or created nnLab entries (mostly just stubs).

      But since at the same time I was also finalizing the writup of an article as well as doing yet some other things, the whole undertaking was a bit time-pressured. As a result, I decided it would be too much to announce every single nnLab edit that I did here on the nnForum.

      So I ask you for understaning that hereby I just collectively announce these edits here: those who care should please scan through the list of blue links here and see if they spot pointers to nnLab entries where they would like to check out the recent edits.

      I think I can guarantee, though, that in all cases I did edits that should be entirely uncontroversial, their main defect being that in many cases they leave one wish for more exhaustive discussion.

    • I've been meaning to write this for a while. Now I need to look at Bourbaki this weekend to explain their approach.

    • Hi guys,

      The situation with my habilitation has been resolved.
      I decided to postone it to more favourable times.

      You can refer to my book and link it.

      Best,

      Frédéric
    • I have created a stub quantum affine algebra as a means to collect some references, alluded to here.

      If there is any expert on the matter around, he or she should please feel invited to add an illuminating Idea-section to the entry.

    • I created types and calculus and seven trees in one. Both entries as yet contain just references.

      It would be nice to have more articles expanding on the reltion of calculus and (higher) category theory /type theory.