In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category M and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in the case when 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.
Some Remarks on Connected Coalgebras
ARDIZZONI, Alessandro;
2009-01-01
Abstract
In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category M and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in the case when 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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