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arxiv: math/9910018 · v2 · submitted 1999-10-05 · 🧮 math.QA · math-ph· math.MP

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Some Topics in coalgebra calculus

A. Borowiec , G. A. Vazquez Coutino
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classification 🧮 math.QA math-phmath.MP
keywords coalgebraactionbeencodualanalysedbicomodulebicomodulescalculus
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We study a coderivation from a cobimodule into a coalgebra. Vector cofields are defined by the action of a codual bicomodule on a coalgebra. This action is induced by a codifferential. A construction of a codual object in the category of bicomodules over a given coalgebra has been proposed. Various notions of duality have been analysed in this context.

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  1. Bicovariant Codifferential Calculi

    math.QA 2026-02 unverdicted novelty 6.0

    Bicovariant codifferential calculi on Hopf algebras reduce to classifying Yetter-Drinfeld submodules, providing a dual to existing differential calculi constructions.