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    • I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?

    • brief category:people-entry for hyperlinking references

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I made a little addition to opposite category, pointing out some amusing nuances regarding the opposite of a VV-enriched category when VV is merely braided. This remark could surely be clarified, but I think you’ll get the idea.

      (In case you’re wondering why I did this, it’s because I needed a reference for “opposite category” in a blog entry I’m writing.)

    • Added redirect for “first-countable”. (Why is there are redirect for “first-countable space”, when that is already the title of the article?)

      diff, v4, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting something, so far some paragraphs of an Idea-section (references to follow in a moment).

      v1, current

    • for completeness, and to make some broken links work

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • some bare minimum on the free coproduct cocompletion.

      The term used to redirect to the entry free cartesian category, where however the simple idea of free coproduct completion wasn’t really brought out.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • The page name should be different because Wigner’s 6j symbols are less relevant to fusion categories so I am not discussing them.

      diff, v2, current

    • am too tired to do it now, but on occasion of an MO discussion:

      remind me to insert at smooth manifold the statement and proof that smooth manifolds are equivalently the locally representable sheaves on CartSp (more precisely: the 𝒢=CartSp\mathcal{G} = CartSp-schemes).

    • The cut rule for linear logic used to be stated as

      If ΓA\Gamma \vdash A and AΔA \vdash \Delta, then ΓΔ\Gamma \vdash \Delta.

      I don’t think this is general enough, so I corrected it to

      If ΓA,Φ\Gamma \vdash A, \Phi and Ψ,AΔ\Psi,A \vdash \Delta, then Ψ,ΓΔ,Φ\Psi,\Gamma \vdash \Delta,\Phi.

    • In response to a zulip comment here, I did a little rewriting of the section concerning biproducts.

      diff, v16, current

    • some trivial edits to opetope (a toc, some hyperlinks)

    • Functor of points approach to algebraic schemes and algebraic groups is in

      • Michel Demazure, Pierre Gabriel, Groupes algebriques, tome 1 (later volumes never appeared), Mason and Cie, Paris 1970; engl. translation Michel Demazure, Peter Gabriel, Introduction to algebraic geometry and algebraic groups, North-Holland mathematics studies 39

      diff, v2, current

      • Pierre Gabriel, La localisation dans les anneaux non commutatifs, Séminaire Dubreil (1959-1960), exposé 2, 1–35 numdam:pdf
      • A. L. Rosenberg, Non-commutative affine semischemes and schemes, Seminar on supermanifolds 26, Dept. Math., U. Stockholm (1988) pdf

      diff, v5, current

    • At affine scheme, the fundamental theorem on morphisms of schemes was stated the other way round. I fixed that.

      As a handy mnemonic, here is a quick and down-to-earth way to see that the claim “Sch(SpecR,Y)CRing(𝒪 Y(Y),R)Sch(Spec R, Y) \cong CRing(\mathcal{O}_Y(Y), R)” is wrong. Take Y= nY = \mathbb{P}^n and R=R = \mathbb{Z}. Then the left hand side consists of all the \mathbb{Z}-valued points of n\mathbb{P}^n. On the other hand, the right hand side only contains the unique ring homomorphism \mathbb{Z} \to \mathbb{Z}, since 𝒪 n( n)\mathcal{O}_{\mathbb{P}^n}(\mathbb{P}^n) \cong \mathbb{Z}.

    • a stub, for the moment just so as to make links work

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Some interesting stuff from https://www.dcs.gla.ac.uk/research/betty/summerschool2016.behavioural-types.eu/programme/DardhaIntroBST.pdf/at_download/file.pdf

      PAnon

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a bare list of references, to be !include-ed into the References-section of relevant entries (such as at superconductivity, qbit, quantum computation and maybe Josephson junction), for ease of synchronizing

      What I am still looking for is an expository reference which would very clearly say that quantum gates in these architectures are electromagnetic pulses, so that quantum circuits are pulse protocols. This is so obvious to all the experts that they tend to forget to say it when explaining the basics…

      v1, current

    • starting something – not ready yet for public consumption, but I need to save

      v1, current

    • added pointer to:

      • Wen-Yuan Ai, Juan S. Cruz, Bjorn Garbrecht, Carlos Tamarit, Absence of CP violation in the strong interactions [arXiv:2001.07152]

        published as: Consequences of the order of the limit of infinite spacetime volume and the sum over topological sectors for C P violation in the strong interactions Phys. Lett. B 822 (2021) 136616 [doi:10.1016/j.physletb.2021.136616]

      • Wen-Yuan Ai, Bjorn Garbrecht, Carlos Tamarit, CP conservation in the strong interactions, Universe 10 5 (2024) 189 [arXiv:2404.16026, doi:10.3390/universe10050189]

      diff, v9, current

    • corrected an error. κ-small filtered \neq κ-filtered

      Shane

      diff, v4, current

    • Fixed link to Evariste Galois in Wikipedia.

      Darren Nicholls

      diff, v3, current

    • I would like to include something on wheeled properads (or wheeled PROPs) in the nlab. It seems to me that a wheeled prop is something like a symmetric monoidal category with duals for every object generated by one object. Is this right? Is there a place in the litterature where i can find the relation between wheeled properads used by Merkulov and some kinds of symmetric monoidal categories with duality?

      Before changing the PROP entry to add this variant, i would like to have a nice reference on this.