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    • only removing the latex markers

      Valeria de Paiva

      diff, v7, current

    • made a bunch of cosmetic edits to formatting and wording (more could be done…)

      diff, v7, current

    • In the category:people-entry “William Lawvere” I have created a subsection “Motivation from foundations of physics” where I want to collect pointers to where and how Lawvere was/is motivated from finding foundations for (classical continuum) physics.

      Explicit evidence for this that I am aware of includes notably the texts Toposes of laws of motion and the introduction to the book Categories in Continuum Physics.

      The Wikipedia entry has this about motivation from physics:

      Lawvere studied continuum mechanics as an undergraduate with Clifford Truesdell. He learned of category theory [...][...] found it a promising framework for simple rigorous axioms for the physical ideas of Truesdell and Walter Noll. [...][...] meeting on “Categories in Continuum Physics” in 1982. Clifford Truesdell participated in that meeting, as did several other researchers in the rational foundations of continuum physics and in the synthetic differential geometry which had evolved from the spatial part of Lawvere’s categorical dynamics program). Lawvere continues to work on his 50-year quest for a rigorous flexible base for physical ideas, free of unnecessary analytic complications.

      Question: Can anyone point me to more on this early phase of the story (graduate student is supposed to start to look into continuum mechanics, starts to wonder “What is a vector field, really?, what a differential equation?” and ends up revolutionizing the foundations of differential calculus)?

    • clarified in the first paragraph the presence and role of the ground field/ring

      (prodded by the comment here)

      diff, v17, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Creating a New note about the Kakeya Conjecture. Just starting.

      Felipe Ponce

      v1, current

    • renamed from “geometric fixed points” to “geometric fixed point spectrum”, which is clearly the better/right entry title

      diff, v3, current

    • Changed ’∞-compact’ to ’sigma-compact’.

      This page is a bit weird, because apparently in 2018 or so I had an idea to generalise the notion in the literature, but didn’t explain it enough for me to reconstruct my idea. I think that the real definition should go here, but I will come back to this soon. Possibly some of the classical stuff works here; I’m thinking the source-fibre-wise Haar measure might exist, but maybe not. But not everything will work, since the space of objects not being locally compact is pretty fatal for getting an overall measure.

      diff, v3, current

    • I have added the adjoint modality of Even⊣OddEven \dashv Odd on (ℤ,≤)(\mathbb{Z}, \leq).

      This example is from adjoint modality (here). But it was actually a little wrong there. I have fixed it and expanded there and then copied over to here.

      diff, v3, current

    • finally a stub for Segal condition. Just for completeness (and to have a sensible place to put the references about Segal conditions in terms of sheaf conditions).

    • brief category:people-entry for hyperlinking references

      v1, current

    • Began stub for Tambara functor. Neil Strickland’s, Tambara Functors, arXiv:1205.2516 seems to be a good reference.

      Seems like it’s very much to do with pullpush through polynomial functors, if you look around p. 23.

      I would try to say what the idea is, but have to dash.

    • I have added a little bit to supermanifold, mainly the definition as manifolds over superpoints, the statement of the equivalence to the locally-ringed-space definition and references.

    • At Fréchet space I have added to the Idea-section a paragraph motivating the definition via families of seminorms from the example of ℝ ∞=lim⟵ nℝ n\mathbb{R}^\infty = \underset{\longleftarrow}{\lim}_n \mathbb{R}^n. And I touched the description of this example in the main text, now here.

    • Unfortunately, I need to discuss with you another terminological problem. I am lightly doing a circle of entries related to combinatorial aspects of representation theory. I stumbled accross permutation representation entry. It says that the permutation representation is the representation in category SetSet. Well, nice but not that standard among representation theorists themselves. Over there one takes such a thing – representation by permutations of a finite group GG on a set XX, and looks what happens in the vector space of functions into a field KK. As we know, for a group element gg the definition is, (gf)(x)=f(g −1x)(g f)(x) = f(g^{-1} x), for f:X→Kf: X\to K is the way to induce a representation on the function space K XK^X. The latter representation is called the permutation representation in the standard representation theory books like in

      • Claudio Procesi, Lie groups, an approach through invariants and representations, Universitext, Springer 2006, gBooks

      I know what to do approximately, we should probably keep both notions in the entry (and be careful when refering to this page – do we mean representation by permutations, what is current content or permutation representation in the rep. theory on vector spaces sense). But maybe people (Todd?) have some experience with this terminology.

      Edit: new (related) entries for Claudio Procesi and Arun Ram.

    • Added:

      Terminology

      There are two inequivalent definitions of Fréchet spaces found in the literature. The original definition due to Stefan Banach defines Fréchet spaces as metrizable complete topological vector spaces.

      Later Bourbaki (Topological vector spaces, Section II.4.1) added the condition of local convexity. However, many authors continue to use the original definition due to Banach.

      The term “F-space” can refer to either of these definitions, although in the modern literature it is more commonly used to refer to the non-locally convex notion.

      The nLab uses “F-space” to refer to the non-locally convex notion and “Fréchet space” to refer to the locally convex notion.

      diff, v9, current

    • the entry braid group said what a braid is, but forgot to say what the braid group is; I added in a sentence, right at the beginning (and fixed some other minor things).

    • a bare minimum, for the moment mainly in order to record some references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have added an observation (here) that complex Hermitian inner product spaces ℋ\mathcal{H} may be regarded as (ℤ/2↷ℂ)(\mathbb{Z}/2 \curvearrowright \mathbb{C})-modules of the form ℋ⊕ℋ *\mathcal{H} \oplus \mathcal{H}^\ast in the topos of ℤ/2\mathbb{Z}/2-sets.

      diff, v6, current

    • Added to Dedekind cut a short remark on the ¬¬\neg\neg-stability of membership in the lower resp. the upper set of a Dedekind cut.

    • Hello, I thought that a new entry would be a good thing. Just a sketch for now.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have added some accompanying text to the list of links at monad (disambiguation).

      One question: in the entry Gottfried Leibniz it is claimed that the term “monad” for a functor on a category with monoid structure also follows Leibniz’s notion of monads. Is this really so? What’s a reference for this claim?

      I am asking because I don’t see how the notion of monoid in the endomorphisms of a category would be related to what Leibniz was talking about. What’s the idea, if there is one?

    • Added more references to arguments involving Galois descent.

      diff, v6, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      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 on arguments

      1. (by Connes) that Heisenberg’s original derivation of “matrix mechanics” and

      2. more generally (by Ibort et al.) that Schwinger’s less known “algebra of selective measurements”

      are both best understood, in modern language, as groupoid convolution algebras,

      to be !include-ed into relevant entries (such as quantum observables and groupoid algebra), for ease of synchronizing

      v1, current

    • a stub entry, for the moment just to make a requested link work at Hilbert’s Theorem 90

      v1, current

    • Create a stub for this concept.

      v1, current

    • a bare minimum, for the time being in order to record the main result of:

      • Richard P. Kent, David Pfeifer: A Geometric and algebraic description of annular braid groups, International Journal of Algebra and Computation 12 01n02 (2002) 85-97 [doi:10.1142/S0218196702000997]

      v1, current

    • brief category:people-entry for hyperlinkingbl references

      v1, current

    • just the other day I was searching for good references on “asymptotic symmetries”, not finding much. But today appears the useful

      and so I am starting an entry hereby

      v1, current

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