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If an underlying-set functor different from the usual one is employed, the categories of multigraphs and of combinatorial systems become cotripleable over the category of sets. The category of multigraphs without loops and a common generalization are also examined.doi:10.1090/s0002-9939-1983-0706504-6 fatcat:efccjxxlbfaltjxvhxosiztfka