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).

nLab > Latest Changes

Show all

781 to 840 of 15191

  1. <
  2. 1
  3. ...
  4. 10
  5. 11
  6. 12
  7. 13
  8. 14
  9. 15
  10. 16
  11. 17
  12. ...
  13. 254
  14. >

    • I gather the following is true and is shown in Battenfield-Schröder-Simpson (pdf), but I haven’t really fully absorbed yet how AdmRepAdmRep is actually embedded in RT(𝒦 2)RT(\mathcal{K}_2).

      The subcategory on the effectively computable morphisms of the function realizability topos RT(𝒦 2)RT(\mathcal{K}_2) is the Kleene-Vesley topos KVKV. The category of “admissible representations” AdmRepAdmRep (whose morphisms are computable functions (analysis), see there) is a reflective subcategory of RT(𝒦 2)RT(\mathcal{K}_2) (BSS) and the restriction of that to KVKV is AdmRep effAdmRep_{eff}

      AdmRep eff ↪ KV ↓ ↓ AdmRep ↪ RT(𝒦 2) \array{ AdmRep_{eff} &\hookrightarrow& KV \\ \downarrow && \downarrow \\ AdmRep &\hookrightarrow& RT(\mathcal{K}_2) }

      This is currently stated this way in the entry function ralizability and computable function (analysis), but please criticize/handle with care, I’ll try to further fine-tune as need be.

    • starting a page for sets whose equality and negation behave as they do in classical mathematics, hence the name

      Anonymouse

      v1, current

    • I added to decidable equality some remarks on the difference between the propositions-as-types version and the propositions-as-some-types version.

    • added to closed monoidal category a proof that the pointwise tensor product on a functor category with complete codomain is closed.

    • starting a minimum, for the moment just to have a place for recording references

      v1, current

    • this is a bare section, spelling out in full detail the construction of the super Lie group integrating the translational part of the “supersymmetry algebra”, namely of the super Poincaré Lie algebra

      (this is of course known to experts, but I am not aware of any literature showcasing how this works in full detail – if such literature exist, please drop a note [the group law itself appears in CAIP99 (2.1) (2.6)])

      this entry is meant to be !include-ed as an Example-subsection into relevant entries, such as at super translation group

      v1, current

    • some observations on Okuyama’s model for the group completion of configuration spaces of points in terms of configurations of open strings with charged endpoints.

      (previous discussion here)

      v1, current

    • it seems difficult to give an original citation for the terminology “Euler vector field”

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • wrote a few lines at differential calculus, just so that the link does point somewhere. Clearly just a stub, to be expanded.

    • starting page on σ\sigma-complete Boolean algebras

      Anonymouse

      v1, current

    • have added (here) as a class of examples the details of the construction of the super-Minkowski Lie group in any dimension,

      by !include-ing the file just announced here

      diff, v19, current

    • added mentioning of the Poincaré lemma for 1-forms over 1-connected domains (here)

      diff, v21, current

    • I added some more information under Frobenius algebra. I would like to add the axioms in picture form, but I haven't figure out how to upload pictures yet. I'm sure I could figure it out if I wanted...

    • have added to conjugation action a detailed exposition of how the conjugation action is the internal hom of actions, here.

    • Quick stub, mostly written from memory.

      v1, current

    • Thanks to a Guest comment here I looked at this page for essentially the first time, and realized that it’s one more thing that’s naturally done in linear constructive mathematics (“complemented subsets” or “disjoint pairs” are the elements of the linear powerset).

      One question: this page says that the disjoint pairs form a “Boolean rig”, but that doesn’t seem right to me. A Boolean rig would, I presume, lack a negation operation entirely; but here we do have an involutive “negation” even though it’s not the “additive inverse”. I would say that the disjoint pairs form a De Morgan algebra, and in fact more generally a *\ast-autonomous lattice. Am I misinterpreting the intended meaning of “Boolean rig”?

      Also, what is the “Handbook of Constructive Analysis” referred to (as a graylink from Bishop \& Bridges)? I can’t find it on google.

      diff, v4, current

    • the link to the Oberwolfach Report pdf had ceased to work. So I have (here) replaced it by a working link and also uploaded the report to the nLab server

      diff, v45, current

    • I created this article so that links from Cheng space point to an actual article on the nLab.

      v1, current

    • The entry monomorphism used to start off saying that a monomorphism is an epimorphism in the opposite category…

      I have polished and expanded the text now, trying to make it look more like an actual exposition and explanation. I have also expanded a little the Examples-section, and similarly at epimorphism.

      These weird kind of entries date from the early days of the nnLab, when none of us saw yet what the nnLab would once be. Back then it was fun to proceed this way, now it feels awkward.

      I hereby pose a challenge to the nnForum community:

      I challenge you to each pick one entry on a basic topic (nothing fancy), go to the corresponding nnLab entry and give it a gentle introductory Idea-section, make sure that the basic motivating examples are mentioned in the order in which the newbie needs to see them, and that the key facts are stated as nicely discernible propositions, best with proof or at least with some helpful pointer, in short, to make the entry a useful read for those readers who would profit from reading it, especially those who do not know the nPOV yet, but might be guided to learn and appreciate it.

    • a bare list of entry names, to be !include-ed into the “Related concepts”-sections of the relevant entries – for ease of cross-linking

      v1, current

    • Ken Brown algebraist, distinguish from Kenneth S. Brown, an algebraic topologist.

      v1, current

    • a bare list of references, to be !include-ed into the References-sections of relevant entries (such as at anyons and at topological order)

      The list means to bring out the wide-spread consideration, in theoretical articles, of anyons whose positions in real space vary on a torus (or even higher genus surfaces) instead of a plane – an assumption that is necessary for many of the intended theoretical conclusions to be valid, but rather dubious as an assumption about actual physical systems (away from simulation).

      The preprint by Gaiotto & Johnson-Freyd at the end is one of the few places that I am aware of where this assumption is questioned, and I included a couple of paragraphs of quote.

      (This all in preparation for an article pointing out that anyonic states can in principle be localized also in more abstract spaces than “position space”, some of which are naturally toroidal, such as the case of reciprocal momentum space for which I took the liberty of pointing to our existing 2206.13563.)

      v1, current

    • Created a stub to record a new article and to satisfy a link.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • some minimum prose on the Kitaev toric code, for the moment mostly just to make the link work and record some references

      v1, current

    • starting page on null types in dependent type theory

      Anonymouse

      v1, current

    • I just noticed and noted that Gabriella Böhm wrote a book, on generalizations in Hopf world,

      • Hopf algebras and their generalizations from a category theoretical point of view, Lec. Notes Math. 2226, Springer 2018

      diff, v9, current

    • Created a stub for cofunctor? with some references.

      v1, current

    • I created hypermonoid, polishing the comments I made in the hypermonoid thread into an article. The last subsection of the article mentions a general technique for constructing hypermonoids which ought to immediately suggest further examples to a quantum group specialist like Zoran, but I am not such a specialist. I also inserted some shameless self-promotion under References.

    • Removed the sentence

      “If XX has decidable equality, then the negation of equality is a (in fact the unique) tight apartness on XX, and any function from XX to any set YY (with any tight apartness on YY) must be strongly extensional.”

      because is not true. Assuming WLPO, Cantor space has decidable equality but the negation of equality is still not the tight apartness relation on Cantor space.

      Anonymouse

      diff, v4, current

781 to 840 of 15191

  1. <
  2. 1
  3. ...
  4. 10
  5. 11
  6. 12
  7. 13
  8. 14
  9. 15
  10. 16
  11. 17
  12. ...
  13. 254
  14. >
Top of Page