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Some Remarks on Connected Coalgebras

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Abstract

In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category \( \mathcal{M} \) and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in the case when \( \mathcal{M} \) is the category of vector spaces over a field K. In particular we characterize when a 0-connected graded bialgebra is a bialgebra of type one.

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Authors and Affiliations

  1. Department of Mathematics, University of Ferrara, Via Machiavelli 35, Ferrara, 44100, Italy

    A. Ardizzoni & C. Menini

Authors
  1. A. Ardizzoni
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  2. C. Menini
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Corresponding author

Correspondence to A. Ardizzoni.

Additional information

Dedicated to Freddy Van Oystaeyen, on the occasion of his sixtieth birthday.

This paper was written while the authors were members of G.N.S.A.G.A. with partial financial support from Mi.U.R.

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Ardizzoni, A., Menini, C. Some Remarks on Connected Coalgebras. Algebr Represent Theor 12, 235–249 (2009). https://doi.org/10.1007/s10468-009-9147-4

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  • DOI: https://doi.org/10.1007/s10468-009-9147-4

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