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

      If Γ⊢A\Gamma \vdash A and A⊢ΔA \vdash \Delta, then Γ⊢Δ\Gamma \vdash \Delta.

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

      If Γ⊢A,Φ\Gamma \vdash A, \Phi and Ψ,A⊢Δ\Psi,A \vdash \Delta, then Ψ,Γ⊢Δ,Φ\Psi,\Gamma \vdash \Delta,\Phi.

    • promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:

      • mentioned more relations to other concepts in the Idea-section;

      • added an Examples-section with a bunch of (classes of) examples;

      • added a list of references. Please add more if you can think of more!

    • I added a discussion of space in Kant’s Transcendental Aesthetics in Critique of Pure Reason.

      By the way, the translation of the quote from Kant in the section “On Aristotelian logic” seem a bit strange: I think the original German sentence was “Begriffe aber beziehen sich als Prädikate möglicher Urtheile auf irgend einen noch unbestimmten Gegenstand” (“But conceptions, as predicates of possible judgements, relate to some representation of a yet undetermined object.”).

      PS The automatic function to create this thread in the nforum did not word.

    • At the old entry cohomotopy used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.

      (We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

    • Urs had earlier started mean value theorem with just a link to Wikipedia. I have now added content. Constructive versions to come, hopefully; for now, see this forum post.

    • Suprema in constructive analysis and their relationship to the antithesis interpretation.

      diff, v19, current

    • added these pointers on application of tensor networks (specifically tree tensor networks) in quantum chemistry:

      • Naoki Nakatani, Garnet Kin-Lic Chan, Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm, J. Chem. Phys. 138, 134113 (2013) (arXiv:1302.2298)

      • Henrik R. Larsson, Computing vibrational eigenstates with tree tensor network states (TTNS), J. Chem. Phys. 151, 204102 (2019) (arXiv:1909.13831)

      diff, v5, current

    • I added the definition and several references on higher dimensional knots under knot.

    • added missing publication data to some references, and added this new reference:

      • D. Melnikov, A. Mironov, S. Mironov, A. Morozov, An. Morozov, A modular functor which is universal for quantum computation, Nucl. Phys. B926 (2018) 491-508 (arXiv:1703.00431)

      diff, v5, current

    • The pages MacNeille real number and MacNeille completion disagree about whether ±∞\pm\infty are MacNeille real numbers. The former says the MacNeille reals are the MacNeille completion of the rationals and hence contain ±∞\pm\infty, whereas the latter says that the MacNeille reals are obtained by “dropping ±∞\pm\infty” from that completion. Which should it be?

      The Elephant also contains a definition of “MacNeille real number” that is more general than a Dedekind cut, but doesn’t contain ±∞\pm\infty: instead of “locatedness” (if a<ba\lt b are rationals then a∈La\in L or b∈Ub\in U) they satisfy “if a<ba\lt b and a∉La\notin L then b∈Ub\in U” and “if a<ba\lt b and b∉Ub\notin U then a∈La\in L”. Since LL and UU are both required to be inhabited, this definition also excludes ±∞\pm\infty. But it’s not clear to me how it’s related to the general definition of MacNeille completion. It would be nice to include a comparison at the page MacNeille real number.

    • am finally giving this book its own category:reference-entry, for ease of compiling and hyperlinking its contents

      v1, current

    • just a stub for the moment, in order to make links work

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

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