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).
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 14th 2020

    Thought I’d start this.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 14th 2020

    I guess we could also say FinCat has enough discrete objects, in that every object admits an essentially surjective functor from a finite set.

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeApr 14th 2020

    There are some papers by Almeida and Weil, e.g. Profinite categories and semidirect products 1, JPAA vol 123, 1998, p. 1-50, that may be relevant. A similar subject is handled in J. P. Jones, Profinite categories, implicit operations and pseudovarieties of categories , again JPAA, vol. 107, 1996. I have not checked if all the terms used there have exactly the same meaning as you are intending, David.

    It is perhaps worth noting that way back in 1980 Dominique Bourn and Jean-Marc Cordier, worked on Distributeurs et la Theorie de la Forme (i.e. abstract shape theory) and used codensity monads in the bicategory Dist. That is in CTDG 21, 161-189. Again I’m not sure if that helps, but it is in the same general area (and Shape Theory seems to be lurking around in some of the stuff being discussed in the Café as well).