### Towards the critical problem: on the coalgebraic relation between sets and multisets

Daniel E. Loeb
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Loeb, D.E., Towards the critical problem: on the coalgebraic relation between sets and multisets, Discrete Mathematics 118 (1993) 157-164. We introduce a generalization of the coalgebra of sets which we call the coalgebra of multisets. After studying this new coalgebra (in fact, a Hopf algebra), we characterize the coalgebra of sets within the coalgebra of multisets by its coalgebraic properties. This gives rise to a new understanding of the relations between sets and multisets.
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