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    • Created the page and added some references

      v1, current

    • I added to excluded middle a discussion of the constructive proof of double-negated LEM and how it is a sort of “continuation-passing” transform.

    • I’ve been inactive here for some months now; I hope this will significantly change soon.

      I have written a stubby beginning of iterated monoidal category, with what is admittedly a conjectural definition that aims to be slick. I am curious whether anyone can help me with the following questions:

      • Is the definition correct (i.e., does it unpack to the usual definition)? If so, is there a good reference for that fact?

      • Assuming the definition is correct, it hinges on the notion of normal lax homomorphism (between pseudomonoids in a 2-category with 2-products). Why the normality?

      In other words (again assuming throughout that the definition is correct), it would seem natural to consider the following type of iteration. Start with any 2-category with 2-products C, and form a new 2-category with 2-products Mon(C) whose 0-cells are pseudomonoids in C, whose 1-cells are lax homomorphisms (with no normality condition, viz. the condition that the lax constraint connecting the units is an isomorphism), and whose 2-cells are lax transformations between lax homomorphisms. Then iterate Mon(), starting with C=Cat. Why isn’t this the “right” notion of iterated monoidal category, or in other words, why do Balteanu, Fiedorowicz, Schwänzel, and Vogt in essence replace Mon() with Monnorm() (where all the units are forced to coincide up to isomorphism)?

      Apologies if these are naive questions; I am not very familiar with the literature.

    • I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

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

      Anonymous

      v1, current

    • http://ncatlab.org/nlab/show/Isbell+duality

      Suggests that Stone, Gelfand, … duality are special cases of the adjunction between CoPresheaves and Presheaves. A similar question is raised here. http://mathoverflow.net/questions/84641/theme-of-isbell-duality

      However, this paper http://www.emis.ams.org/journals/TAC/volumes/20/15/20-15.pdf

      seems to use another definition. Could someone please clarify?

    • added to G2 the definition of G2 as the subgroup of GL(7) that preserves the associative 3-form.

    • Fix naming of index variable to match index on expression inside.

      Greg Langmead

      diff, v3, current

    • Added to noetherian ring a homological chacaterization: a ring is Noetherian iff arbitrary direct sums of injective modules are injective.

    • Added more lowbrow, quicker-to-understand definition of “coherent ring”.

      diff, v3, current

    • starting page on 𝒜-rings

      Anonymouse

      v1, current

    • I have spelled out the proofs that over a paracompact Hausdorff space every vector sub-bundle is a direct summand, and that over a compact Hausdorff space every topological vector bundle is a direct summand of a trivial bundle, here

    • starting page on 𝒜-groups

      Anonymouse

      v1, current

    • starting page on 𝒜-monoids

      Anonymouse

      v1, current

    • starting page on the cartesian product of 𝒜-sets

      Anonymouse

      v1, current

    • starting page on the tensor product of 𝒜-sets

      Anonymouse

      v1, current

    • starting page on affine sets

      Anonymouse

      v1, current

    • starting a disambiguation page on affine functions

      Anonymouse

      v1, current

    • Added appropriate axioms for the various definitions of affine space, along with another definition in terms of a single quaternary operation.

    • starting page on affine functions in the antithesis interpretation of constructive mathematics

      Anonymouse

      v1, current

    • starting page on obtuse triangles

      Anonymouse

      v1, current

    • starting page on right triangles since the paper

      • John Baez, The Moduli Space of Acute Triangles, Notices of the American Mathematical Society, Volume 71, Number 5, pages 664-665, May 2024. (arXiv:2407.06201, pdf)

      talks about right triangles too

      Anonymouse

      v1, current

    • Deleted from the History section three consecutive paragraphs begining with “More precisely, when a moduli space…” that appeared in verbatim copy in the Idea section.

      diff, v33, current

    • Adding reference

      • John Baez, The Moduli Space of Acute Triangles, Notices of the American Mathematical Society, Volume 71, Number 5, pages 664-665, May 2024. (arXiv:2407.06201, pdf)

      Anonymouse

      diff, v22, current

    • I have expanded vertex operator algebra (more references, more items in the Properties-section) in partial support to a TP.SE answer that I posted here

    • starting page on acute triangles

      Anonymouse

      v1, current

    • We should have an entry on large N limit gradually. But sometimes it can be treated as a semiclassical limit. I quoted a reference by Yaffe where I originally read of that approach to the entry semiclassical expansion.

    • starting page on constructible numbers

      Anonymouse

      v1, current

    • Added section on triangles in constructive mathematics

      Anonymouse

      diff, v7, current

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

      Anonymous

      v1, current

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

      Anonymous

      v1, current

    • Created a page to handle a link in another page.

      v1, current

    • a bare minimum, for the moment just so as to make the link work

      v1, current

    • some bare minimum, for the moment just so that the link works

      v1, current

    • this entry used to be titled just conductor, but have now made that a category:disambiguation-page, for obvious reasons

      v1, current

    • Came across this early page and neatened it up a little.

      diff, v2, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • starting article on principal ideal rings

      Anonymouse

      v1, current

    • Making this page

      Natalie Stewart

      v1, current

    • See Day convolution

      I started writing up the actual theorem from Day’s paper “On closed categories of functors”, regarding an extension of the “usual” Day convolution. He identifies an equivalence of categories between biclosed monoidal structures on the presheaf category VAop and what are called pro-monoidal structures on A (with appropriate notions of morphisms between them) (“pro-monoidal” structures were originally called “pre-monoidal”, but in the second paper in the series, he changed the name to “pro-monoidal” (probably because they are equivalent to monoidal structures on the category of “pro-objects”, that is to say, presheaves)).

      This is quite a bit stronger than the version that was up on the lab, and it is very powerful. For instance, it allows us to seamlessly extend the Crans-Gray tensor product from strict ω-categories to cellular sets (such that the reflector and Θ-nerve functors are strong monoidal). This is the key ingredient to defining lax constructions for ω-quasicategories, and in particular, it’s an important step towards the higher Grothendieck construction, which makes use of lax cones constructed using the Crans-Gray tensor product.

    • I wanted to be able to use the link without it appearing in grey, so I created a stub for general relativity.

    • starting article about the ascending chain condition on principal ideals

      Anonymouse

      v1, current

    • starting article on atomic domains

      Anonymouse

      v1, current

    • starting page on commutative operations of arbitrary finite arity

      Anonymouse

      v1, current

    • Beginning an article on δ-rings in the sense of Joyal, partly spurred by the recent additions by Anton Hilado.

      v1, current