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The following material is discussed in this paper: Incidence Coalgebras for PO sets; Reduced Boolean Coalgebras; Divided Powers Coalgebra; Dirichlet Coalgebra; Eulerian Coalgebra; Faà di Bruno Bialgebra; Incidence Coalgebras for Categories; The Umbral Calculus; Infinitesimal Coalgebras; Creation and Annihilation Operators; Point Lattice Coalgebras; Restricted Placements; Cleavages; and Hereditary Bialgebras.
Joni et al. (Mon,) studied this question.
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