Not signed in (Sign In)

Start a new discussion

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 bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration 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 kan lie-theory limit 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 newpage nlab nonassociative noncommutative noncommutative-geometry number-theory object 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 5th 2018

    Had a look at some literature and found of course that it’s vast, so have added some findings.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 5th 2018

    added hyperlinks to a bunch of keywords.

    (It’s so easy to include keywords in double brackets!, and so very useful for the reader!, especially for newbies to the topic. I suggest making it a habit.)

    diff, v6, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 5th 2018

    I’m wondering now how consistent is the naming in this neck of the words, especially transporter category and Frobenius category. The latter does not mean Frobenius category. We’re coming close here to the intricate world of fusion systems.

    I’ve left a reference where I took the terminology from.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2021

    Have moved discussion of Properties out of the Definition-section.

    Have replaced the tom Dieck-reference item with a hyperlinked version:

    (which means I had to remove the experimental bibtex functionality, for the time being)

    and I changed the wording around that reference:

    The term “EI-category” is not actually in that book, is it? What is there, on p. 73, is the explicit observation that “endomorphisms are automorphisms” on the orbit category and its relatives.

    So I have made the wording refer to that verbiage on that page now, instead. But let me know if I am missing something.

    diff, v11, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeMay 10th 2021
    • (edited May 10th 2021)

    Does anyone have any nicer names for this concept? I find “EI” to be a confusing term, because “I” could stand for either “isomorphism” or “identity” (the latter being the defining property of one-way categories). An actual adjective would be more aesthetic as well.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeMay 10th 2021

    It’s a pretty standard term, unfortunately. (Perhaps you meant to refer to gaunt categories for the other notion; they don’t have to be direct.)

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 11th 2021

    Perhaps you meant to refer to gaunt categories for the other notion; they don’t have to be direct.

    Oh, the nLab entry for one-way categories is a little misleading at the moment, because they’re defined on the page for direct categories; however, one-way categories do not have to be direct. Perhaps it would be better to give them their own page.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeMay 11th 2021

    Yes, I realized actually gaunt is somewhat different, that means every isomorphism is an identity, but you mean every endomorphism is an identity.

    I don’t think I’ve ever heard anyone talk about one-way categories that aren’t direct, but I guess the definition allows that. The terminology seems somewhat strange in that case, though; what’s “one-way” about a category with this sort that isn’t direct? In particular, it doesn’t have to be skeletal, does it?

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeMay 11th 2021

    The terminology seems somewhat strange in that case, though; what’s “one-way” about a category with this sort that isn’t direct? In particular, it doesn’t have to be skeletal, does it?

    I agree: “one-way” doesn’t seem like an accurate description unless you also impose that the category is skeletal (in which case you have an acyclic category).

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 27th 2021

    added (here) pointer to one more example: tom Dieck’s fundamental category of a GG-space

    diff, v14, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 27th 2021

    added a couple more references on representation theory of EI-categories, and gave the list of references a little more structure

    diff, v16, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)