Abstract
The article studies the category of multisets. The stability of strict epimorphisms in Cartesian squares and strict monomorphisms in coCartesian squares is proved. These results allow us to construct categories of correspondences and cocorrespondences of multisets in which the category of functional morphisms is equivalent to the category of multisets. Within the framework of the correspondence categories, the description of equivalence relations and congruencies on multisets is given. The category of multisets is not exact: according to some equivalence relations, a multiset cannot be factorized. Using the technique of ordered categories with involution, the authors construct a minimal embedding of the category of multisets to the exact category, which is universal. Depending on whether correspondences or noncorrespondences are used, this embedding preserves finite limits or co limits.
Published Version
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