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    • Starting stub on the Heine-Cantor theorem

      Anonymouse

      v1, current

    • found a mathoverflow question where people in the answers are talking about σ\sigma-topological groups and sets equipped with a σ\sigma-topology, so decided to create an article on such objects.

      v1, current

    • I’m interested in editing Mac Lane’s proof of the coherence theorem for monoidal categories, as I recently went through all the gory details myself and wrote it up. I was wondering if anybody has any thoughts on what should be left alone with regard to any future changes. Many people clearly put in a lot of work into the page, but it looks like people got busy and it hasn’t been updated in a while.

      I think the first few paragraphs are fine, but I think the rest is a bit wordy, it could be more formal, and notation could be changed (very slightly) to be less clunky. I specifically want to make the current document more formal (e.g., saying “Definition: blah blah”), include some nice diagrams, change the notation (e.g., to avoid using double primes, to avoid denoting a monoidal category as B since I think the letter M pedagogically makes more sense), and complete the incomplete entries at the bottom. I’m not really sure if anyone would be against such changes, hence my inquiry.

    • starting article on A1-cohesive homotopy type theory, where an affine line 𝔸 1\mathbb{A}^1 is used instead of ℝ\mathbb{R} in real-cohesive homotopy type theory, and where the shape modality is 𝔸 1\mathbb{A}^1-localization rather than ℝ\mathbb{R}-localization.

      Anonymous

      v1, current

    • starting page on axiom C0 in cohesive homotopy type theory

      Anonymous

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • stub – for the moment just as to satisfy links

      v1, current

    • starting stub on fractured homotopy type theory

      Anonymouse

      v1, current

    • Fixed a dead link to the Lack-Power paper

      Anonymous

      diff, v14, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a stub entry, for the moment just to make the link work

      v1, current

    • For start only the classical Capelli identity

      v1, current

    • at monadicity theorem in the second formulation of the theorem, item 3, it said

      CC has

      I think it must be

      DD has

      and have changed it accordingly. But have a look.

    • starting something on isometric immersions

      — mainly I was trying to track down a reference that would clearly state that orthonormal “adapted” or “Darboux” (co)frames (here) always exist locally for an immersion into a Riemannian manifold.

      What I found so far is

      Mastrolia, Rigoli & Setti 2012, p. 33, where this is claimed, but just in passing

      and

      Chen & Giron 2021, Thm. 2.2, where this is stated in the generality of sequences of immersions, which makes it hard to recognize the simple statement behind all the analytic fine-print.

      v1, current

    • created a bare minimum at harmonic map (for the moment just so as to have a place to record the reference given there)

    • brief category:people-entry for hyperlinking references

      v1, current

    • added pointer to:

      • John M. Lee, Riemannian manifolds. An introduction to curvature. Graduate Texts in Mathematics 176 (1997), Springer. ISBN: 0-387-98271-X. Second Edition (retitled): Introduction to Riemannian Manifolds (2018), Springer. ISBN: 978-3-319-91754-2 (doi:10.1007/978-3-319-91755-9)

      diff, v16, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • A very brief description of the Ehrenfeucht-Fraisse comonad, as defined by Abramsky-Shah, which described the Ehrenfeucht-Fraisse game.

      Eigil Rischel

      v1, current

    • Partially ordered abelian groups whose partial order is a pseudolattice

      Anonymous

      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

    • Updating reference to cubical type theory. This page need more work.

      diff, v55, current

    • The entry unit of an adjunction had a big chunk of mixed itex+svg code at the beginning to display an adjunction. On my machine though the output of that code was ill typeset. So I have removed the code and replaced it by plain iTex encoding of an adjunction.

      (Just in case anyone deeply cares about the svg that was there. It’s still in the history. If it is preferred by anyone, it needs to be fixed first.)

    • Gave concrete formula for coextension of scalars and a case where extension and coextension agree.

      diff, v5, current

    • In some thread here (which I seem to have lost) there was the open question of whether the Selberg zeta function is indeed the zeta function of the corresponding Laplace operator. The answer is of course Yes, I have added the following paragraph to zeta function of a Riemann surface:

      That the Selberg zeta function is indeed proportional to the zeta function of a Laplace operator is due to (D’Hoker-Phong 86, Sarnak 87), and that it is similarly related to the eta function of a Dirac operator on the given Riemann surface/hyperbolic manifold goes back to (Milson 78), with further development including (Park 01). For review of the literature on this relation see also the beginning of (Friedman 06).

      (the links will only work from within the entry)

    • starting page on definitional isomorphisms

      Anonymouse

      v1, current

    • have touched wording, formatting and hyperlinking of this entry, trying to streamline a bit

      diff, v3, current

    • I have touched wording, formatting and hyperlinking, trying to brush-up this entry. But there is still room to do more.

      diff, v6, current

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

      v1, current

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

      v1, current

    • Corrected an arithmetic error in the last section.

      diff, v14, current

    • expanded the discussion at equivariant homotopy theory

      • expanded the statement of the classical Elmendorf theorem

      • added the statement of the general Elmendorf theorem in general model categories

      • added remarks on G-equivariant oo-stacks, as special cases of this

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

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