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    • created Duskin nerve.

      Would like to cite page and verse of Duskin’s artcile for where he defines something like the free bicatgeory on a simplex, but don’t appear to have the patience to dig through the document right now.

    • I wrote fan theorem a while back but I never got around to announcing (or finishing what I wanted to do with it, but that’s OK).

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

      v1, current

    • Made a start. Hopefully some functional analysts can improve it.

      v1, current

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

      v1, current

    • Changed reference details since the book is now on the arXiv.

      diff, v4, current

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

      v1, current

    • here are Eh’s wen pages and research career

      https://scholar.google.com/citations?user=00V0JVYAAAAJ&hl=en

      https://old.inspirehep.net/author/profile/E.Hatefi.1

      https://orcid.org/0000-0003-1939-8912

      annonymos

      v1, current

    • The minute before I had entered offline territory a few days ago, I had expanded the list of examples of (commuting) diagrams at diagram.

    • some minimum, for the moment just so as to record the recent results by the FIRE-2 computer simulation

      v1, current

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

      v1, current

    • have tried to complete the list, under “Selected writings”, of the articles referenced on the nnLab, and have tried to make all of them hyperlinking Lewis’ name

      diff, v5, current

    • This page was titled “Seifert-van Kampen theorem” and contained nothing but the link to van Kampen theorem. I am “deleting” (clearing, renaming and thereby orphaning) it hereby and have instead created the proper redirect

      diff, v3, current

    • Now I am working on the next chapter of “geometry of physics”: geometry of physics – supersymmetry.

      A fair bit of material is in place now, but much is missing still. This here is mainly in case you are watching the logs and are wondering. At this point, if anyone has any edits to suggest (typo fixing or more substantial) maybe best to not touch the file yet but to tell me about it. Thanks!

    • I have renamed the entry on the ∞\infty-topos on CartSp topCartSp_{top} into Euclidean-topological infinity-groupoid.

      Then in the section Geometric homotopy I have written out statement and proof that

      1. the intrinsic fundamental ∞\infty-groupoid functor in ETop∞GrpdETop \infty Grpd sends paracompact topological spaces to their traditional fundamental ∞\infty-groupoid

        Π ETop∞Grpd(X)≃Π Top(X)≃SingX \Pi_{ETop \infty Grpd}(X) \simeq \Pi_{Top}(X) \simeq Sing X;

      2. more generally, for X •X_\bullet a simplicial topological space we have

        |Π ETop∞Grpd(X •)|≃|X •| |\Pi_{ETop \infty Grpd}(X_\bullet)| \simeq |X_\bullet| ,

        where on the left we hve geometric realization of simplicial sets, and on the right of (good) simplicial topological spaces.

    • am giving this, finally, its own little page

      v1, current

    • have added the original articles on geometric quantization and on diffeological spaces to the list of “Selected writings”

      diff, v5, current

    • just to make edit signatures be hyperlinked

      v1, current

    • Just a definition (hope I got it right) and a couple properties. I wasn’t sure how to set up the redirects; currently “modest set” redirects here while “PER” redirects to partial equivalence relation, but other suggestions are welcome.

      v1, current

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

      v1, current

    • the old entry representation contained an old query box with some discussion.

      I am hereby moving this old discussion from there to here:

      +– {: .query} I don't agree with this D≔Aut(V)D \coloneqq Aut(V) business. A kk-linear representation of a group GG is a functor from BG\mathbf{B}G to kVectk Vect, period. Because BG\mathbf{B}G has one object (or is pointed), we can pick out an object VV of kVectk Vect, and it was remiss of me not to mention this (and the language ‘on VV’ vs ‘in DD’. But we usually don't want DD to actually be Aut(V)Aut(V) instead of kVectk Vect; when doing representation theory, we fix GG and fix kk (or fix DD in some other way), but we don't fix VV. —Toby

      If you look at the textbooks of representation of groups, then they start with representation of groups as homomorphisms of groups, that is just functors. Then they say, that usually the target groups are groups of automorphisms of some other objects. And at the end they say that one usually restricts just to linear automorphisms of linear objects when linearizing the general problematics to the linear one. Now the fact that in some special case there is a category which expresses the same fact does not extend to other symmetry objects, like for representations of vertex operator algebras, pseudotensor categories etc. I mean End(something) or Aut(something) is just inner end in some setup like in closed monoidal category, but there are symmetries in mathematics which have a notion of End of Aut for a single object but do not have good notion of category one level up which has inner homs leading to the same End or Aut. Conceptually actions are about endosymmetries or symmetries (automorphisms) being reducable to categorical ones but not necessarily, I think. In a way you say that you are sure that any symmetry of another object can be expressed internally in some sort of a higher category of such objects, what is to large extent true, but I am sure not for absolutely all examples.

      • I can’t recall ever seeing group homomorphisms ρ:G→H\rho\colon G \to H described in general as ’representations’, but I have limited experience; I should look at some more textbooks. The one that I learnt the subject from, Serre's Linear Representations of Finite Groups, looked only at representations on vector spaces from the beginning, but its title suggests a bias that might explain that. (^_^)

      (for “on” terminology:) Ross Street uses monads in a 2-category and monads on a 1-category and I know of no objects in category theory.

      • Yes, this is analogous to representation in a category vs on an object in such a category. (But what do you mean by ’I know of no objects in category theory’?)

      Another important thing is that the endomorphisms are by definitions often equipped with some additional (e.g. topological) structure which is not necessarily coming from some enrichement of the category of objects. –Zoran

      • Good point.

      (Zoran on word “classical representation” being just for groups: so the representations of associative algebras, Lie algebras, Leibniz algebras, topological groups, quivers, are not classical ??).

      • I thought that they came later, but maybe not. I added ’of groups’ to fix/clarify. —Toby =–

    • I am starting to bring (infinity,n)-category into shape. So far I have

      • rewritten the Idea-section

      • added a bare minimum of the axiomatic characterization

      • added references

      • also polished n-category a bit.

      My plan ist to add now technical details to the entry. Let’s see how far I get.

    • I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.

    • Added a description of the Sweedler hom and Sweedler product.

      diff, v29, current

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