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 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 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 nforum 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 sheaves 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).

nLab > Latest Changes: locally graded category

Bottom of Page

1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeJun 5th 2023

    Create a stub for this concept.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeJun 5th 2023

    Mention locally indexed categories and a connection to simplicially enriched categories.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2023

    I have touched wording, formatting and hyperlinking and completed the publication data for the articles by Wood and Riehl.

    Mainly I took the liberty of adjusting the wording of this paragraph:

    This gives an abstract proof of the fact that simplicially enriched categories can be viewed as functors into the category of small categories and identity-on-objects functors (see Proposition 1.2.3 of Riehl).

    to the following:

    For example, with Levy (2019), slide 21 this gives an abstract proof of the standard fact that simplicially enriched categories can be viewed as those simplicial objects in Cat which take value in identity-on-objects functors (e.g. Riehl (2023), Prop. 1.2.3).

    Here I think it’s Levy’s slide 21 that you mean to be referring to. But that slide is most brief, this would deserve a more detailed reference.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeJun 6th 2023

    You’re right, the remark probably comes across as a little cryptic at the moment. I’ll try to find time to expand upon it later.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2023

    All right, thanks.

    A good abstract discussion of the relation between sSetsSet-enriched categories and simplcial objects in categories would be worthwhile to point to also from sSet-enriched category and enriched groupoid, etc.:

    The reflection of this equivalence in the literature is somewhat curious (as reflected eg. in the references here): Everybody must feel it’s too trivial to dwell on (also the proposition by Riehl that you point to doesn’t really say more than that) and nobody takes the extra step of categorical algebra to “show that it’s trivially trivial”.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeDec 15th 2023

    Spelled out the definition of a locally graded category.

    diff, v4, current

1 to 6 of 6

  1.