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    • [spam]

    • Initial writeup to satisfy a broken link.

      v1, current

    • Added a link for « Blue and Brown Books ». I’ll try to create this page later, and when I will have understood the book.

      diff, v3, current

    • there was an X veeX^{vee} that I replaced with X ∨X^{\vee}

      Joe M

      diff, v7, current

    • Added the Yoneda-embedding way to talk about group objects and hence supergroups.

    • brief category:people-entry for hyperlinking references

      v1, current

    • Wrote that the affine spectrum is the right adjoint to the global section functor from the commutative locally ringed spaces to commutative rings, what is the abstract way to characterize this functor.

      diff, v9, current

    • More clarification/delimitation of the named results.

      diff, v5, current

    • An algebraist at King’s College.

      v1, current

    • Person entry on the analyst rather than algebraist Birkhoff.

      v1, current

    • Added a bit, including the original reference by G. B.

      diff, v7, current

    • I added some simpler motivation in terms of the basic example to the beginning of distributive law.

    • 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

    • changed title to match more systematic naming convention

      diff, v14, 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

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