Categorical construction of comodule category of FRT algebra

Let B denote the braid groupoid, with objects being non-negative integers nZ0 and morphisms B(n,n)=Bn given by the braid group. Let C be a cocomplete rigid symmetric monoidal abelian category and F:BC a monoidal functor. Moreover, let C:=bBF(b)F(b) be the coend of F and V:=F(1).

Is there a “purely categorical construction” of a category CV , s.t. there is a braided monoidal equivalence CVCC to the comodule category of the coalgebra C (which is actually a coquasitriangular bialgebra).

Here, by “purely categorical construction” I mean (up to order and missing intermediate steps) something along the lines of

  • take free monoidal subcategory of C generated by V.
  • close it under direct sums
  • take the Karoubi envelope


Source : Link , Question Author : Bipolar Minds , Answer Author : Community

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