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.
    • CommentAuthorDavidCarchedi
    • CommentTimeAug 29th 2017

    Dear nLab folks,

    An advanced undergrad with some familiarity with category theory and algebraic topology is interested in doing some additional reading this semester, on their own. I was looking for some suggestions. I seem to remember there were some “discussion notes” that John Baez had, where they read like a conversation, because they were actually a back and forth between him and a student, but I can’t seem to find them. Other suggestions are welcome as well. Thanks in advance.

    Best,

    Dave

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 29th 2017

    John used to do Oz and the Wizard dialogues, such as this one for general relativity. I’m not sure where else the Wizard appears again.

    If you mean specifically algebraic topology, there’s his course. For a range of seminars, see here.

    • CommentRowNumber3.
    • CommentAuthorHarry Gindi
    • CommentTimeAug 30th 2017
    • (edited Aug 30th 2017)

    Throw the students into the thick of it. I really liked Angelo Vistoli’s notes on fibered categories, stacks, and descent, and I moved onto Lurie’s HTT from there way back when.

    I would not suggest HTT for a first course though. Joyal’s unreleased book on quasicategories is a much friendlier treatment of the basics because it actually bothers to go through the simplicial combinatorics and arguments. Personally I did not like Categories for the Working Mathematician. I found it extremely dry.

    I think that John Baez’s Oz thing is too much of a baby treatment of the stuff. The best way to learn this stuff is to jump in headfirst and then recurse backwards into references when you don’t understand the detail of a proof.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 30th 2017

    Why not Emily’s CT textbook? Or even her first book?

    • CommentRowNumber5.
    • CommentAuthorDavidCarchedi
    • CommentTimeAug 30th 2017

    Thanks for the suggestions so far. He’s already gone through a lot of Emily Riehl’s book, as I used it in the course on category theory I taught that he audited, and he’s taken algebraic topology with me out of May’s book.. Vistoli’s notes are quite nice though, that’s a good idea.

    Thanks for the Baez links David.

    Any other recommendations would be great as well.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeAug 30th 2017

    If you’re aiming for a more category-theoretic direction, I like Steve Lack’s “2-categories companion”, and Kelly’s book on enriched category theory is also good.

    In a rather different direction, there is of course the HoTT book too… (-:O

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeAug 30th 2017
    • (edited Aug 30th 2017)

    David, you are welcome to have a copy of the notes I started for a course in Ottawa some years ago (known as the Crossed Menagerie) There is a short version on the Lab but a lot of other stuff has been added since that was put there in 2010. The notes try to use both a modern model category type of approach (although the reader is often assumed to know the meaning of the terms from that language) as well as the more combinatorial descriptions using cocycles, etc. There is a lot of simplicial stuff in them as well also some of the crossed complex theory that is not easy to find in the literature. I leave lots of hints for explorations away from the notes, and initiations to other approaches as I felt that a student has to be able to use several different mathematical languages to swim well in these waters. They thus tackle some classical topics as well as stacks, etc.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 30th 2017

    Has your student worked through Urs’s courses? You can see them listed at the start of Introduction to Stable Homotopy Theory.

    • CommentRowNumber9.
    • CommentAuthorDavidCarchedi
    • CommentTimeSep 14th 2017

    @Mike: Thanks, I’ll pass that on. I actually haven’t read those myself, so I should have a look. I think HoTT might be a bit out of reach at the moment though.

    @Tim, sorry for the delay. I’d love a copy of your notes. (Even for myself). I’ll send you an email.

    @DC: Thanks for the link. I think he’d need to take the algebraic topology sequel I’m teaching next semester before tackling stable homotopy though, but I’ll be sure to point him (and the rest of my class) towards Urs’ notes.

    • CommentRowNumber10.
    • CommentAuthorDavidCarchedi
    • CommentTimeSep 14th 2017

    @Tim: Can’t find your email. Mine is davidcarchedi@gmail.com

    • CommentRowNumber11.
    • CommentAuthorTim_Porter
    • CommentTimeSep 14th 2017
    • (edited Sep 14th 2017)

    @David: remember the notes change… but more frequently than my e-mail. I will send you the notes, and thus my e-mail!

    (Edit: some hours later: I have sent you the notes.)

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 14th 2017

    @David: the notes I pointed to in #8 concern more than stable homotopy. Note the two background files and the prelude.

    • CommentRowNumber13.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 14th 2017

    @Tim may I have an updated version of the notes, too?

    • CommentRowNumber14.
    • CommentAuthorTim_Porter
    • CommentTimeSep 14th 2017

    Of course, they will be speeding their way to Oz shortly. (There are not that much more added since the earlier version you know of but …. )

    • CommentRowNumber15.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 14th 2017

    Thanks!