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 definitions 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 nlab 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 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.
    • CommentAuthoranuyts
    • CommentTimeJan 28th 2020

    Added a lemma about fully faithful functors.

    Sorry for the mess, there does not seem to be a way to preview edits.

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 29th 2020

    Thanks. How do you mean ’the mess’? I introduced a space in ’RL’, which makes it work in Itex, RLR L.

    • CommentRowNumber3.
    • CommentAuthoranuyts
    • CommentTimeMar 3rd 2023

    Link to free cocompletion and lax-idempotent 2-monad.

    diff, v5, current

    • CommentRowNumber4.
    • CommentAuthoranuyts
    • CommentTimeMar 3rd 2023
    @David_Corfield: Regarding "the mess": I probably added the lemma in several partial edits but it seems nLab has a good way to wrap these up automatically.
    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeMar 3rd 2023

    Might this content be useful to collapse into the main page on category of presheaves?

    • CommentRowNumber6.
    • CommentAuthoranuyts
    • CommentTimeMar 5th 2023

    Replace equalities with (natural) isomorphisms.

    diff, v6, current

    • CommentRowNumber7.
    • CommentAuthoranuyts
    • CommentTimeFeb 16th 2024

    Functoriality w.r.t. profunctors.

    diff, v7, current

    • CommentRowNumber8.
    • CommentAuthoranuyts
    • CommentTimeFeb 16th 2024

    Explain constituent functors of adjoint triple.

    diff, v7, current

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 1st 2025

    Since this is rather light on details about DD,

    Given a small category CC, one can consider the category of presheaves PSh(C,D)PSh(C, D) valued in some category DD. Given some assumptions on DD, any functor…,

    I asked on Zulip and someone says these conditions on DD are to do with its possessing colimits (and limits) of size CC. Can we say something precise here?

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 1st 2025

    Yes, the condition is that the Kan extensions exist, which are mentioned in the next line, which for pointwise Kan extension means that DD has the required (co)limits.

    Of course, the entry could say this more explicitly.

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 1st 2025

    I see. I’ll add the information at the earlier spot then.

    diff, v9, current