Associated Graded Algebras and Coalgebras

We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal categories.

💡 Research Summary

The paper develops a systematic theory of associated graded coalgebras and algebras for a bialgebra situated in an abelian braided monoidal category. Starting with a bialgebra (B) and either a sub‑bialgebra (A\subseteq B) or a quotient bialgebra (\pi\colon B\to C), the authors introduce natural filtrations: the powers of (A) (the “(A)-adic” filtration) and the powers of the kernel of (\pi). From these filtrations they construct the associated graded objects
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