Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 2nd 2020

    redirect

    diff, v9, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 2nd 2020

    He is now one of the main advocates of higher category theory in the United States.

    really? Is this meant to mean the “most senior advocate”? As opposed to Lurie etc? May has even poured scorn over on MO on people who jump to model-independent \infty-categorical explanations.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 2nd 2020

    Maybe “of low-dimensional higher category theory”, as per his more recent praise of 2-category theory (can’t find the link now, though).

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 2nd 2020
    • (edited May 2nd 2020)

    I’d be interested to see that.

    I seem to recall Lurie saying he didn’t really use 2-category theory, despite (,2)(\infty, 2)-Categories and the Goodwillie Calculus.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 2nd 2020

    Found it: slide 2 of

    • Peter May, Input for derived algebraic geometry: equivariant multiplicative infinite loop space theory Banff, February 18, 2016 (pdf)

    announces that:

    2-category theory ROCKS

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 2nd 2020

    Thanks. And here is what I was mentioning by Lurie:

    I don’t think I’d consider that an honest application as of yet: the formalism of (infty,2)-categories is only used at the end to restate the earlier results, not to prove or improve upon them. However, I believe that the formalism of (infty,2)-categories will be extremely useful for getting deeper into the Goodwillie calculus (studying higher derivatives, understanding the chain rule, and so forth).

    Another endorsement then.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 2nd 2020

    To come back to the entry on Peter May:

    I agree with David R. that the statement

    He is now one of the main advocates of higher category theory in the United States.

    seems dubious. Maybe the modification as I suggested

    He is now one of the main advocates of 2-category theory…

    is getting closer to the truth. But do we have more than one enthusistic remark in one public talk four years ago?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 4th 2020

    This will be my last contribution here, but just for completeness:

    • The line in question in #2 was added in revision 3, way back in June 2009. This was around May co-editing “Towards Higher Categories

    • An example of the “scorn” on \infty-category theory mentioned in #2 in here.

    I won’t edit the entry. But my suggestion is: Best not to claim what anyone is an “advocate” of, but instead to give primary sources of their writing: This book and that MO comment should really be linked to in the entry.

  1. remove hilariously false claim

    Anonymous

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 4th 2020

    Re #9, a particularly annoying tone! If you’d bothered to read the thread, it was in the process of being altered or removed.

    In that Peter May had been one of the two leads on the summer school ’nn-Categories: Foundations and Applications’ at the University of Minnesota (Minneapolis,7-18 June 2004) and editor of the book Urs mentions, it wasn’t ’hilariously false’. The meaning of ’higher category theory’ changed.

    Try and contribute in a more collegial spirit.

    • CommentRowNumber11.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 4th 2020

    @David this person may not have been aware of the discussion thread, and just edited the page directly (for instance, I would not be a bit surprised if May himself did that edit, being alerted to the existence of the statement by a third party).

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 5th 2020

    Yes, perhaps. The timing is quite a coincidence though, unless something external prompted you to write #2.

    • CommentRowNumber13.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 5th 2020

    No, just looking at the page after Dmitri’s edit. I hadn’t seen the contentious claim before.

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2020
    • (edited May 5th 2020)

    I had had the same thought as #11, but checked that the source IP seems to have been from Belgium.

    And not to belittle politeness of words, I’ll say that it’s decent to take the responsibility of acting where action is clearly called for.

    Therefore I have now contradicted my own plea of #8 and did edit the entry on the issue here, after all. Here is what I added. Hopefully this inspires somebody closer to Peter May to chime in and expand/improve:

    Peter May’s work makes extensive use of enriched- and model-category theory as power tools in algebraic topology, notably in discussion of highly structured spectra in MMSS00’s Model categories of diagram spectra (for exposition see Introduction to Stable homotopy theory – 1-2), or in the discussion of K-theory of permutative categories. While he has co-edited a book collection on higher category theory (Baez-May 10) and eventually had high praise (May 16) for 2-category theory as a tool in algebraic topology/higher algebra, he has vocally warned against seeing abstract (∞,1)-category theory as a replacement of concrete computations in model category-theory (P. May, MO comment Dec 2013).

    • CommentRowNumber15.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 5th 2020

    @Urs

    that’s excellent, thanks.

    • CommentRowNumber16.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 5th 2020

    Politeness is free. Anyway, something good came out of it.

    • CommentRowNumber17.
    • CommentAuthorMike Shulman
    • CommentTimeMay 19th 2020

    Coming to this thread a little late, the current version looks pretty good to me.

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeJan 11th 2021

    added the references on ring spectra to the list of “Selected writings”

    diff, v16, current