Multisets and Distributions

Dexter Kozen; Alexandra Silva

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arXiv · 2301.10812

Multisets and Distributions

Dexter Kozen·Alexandra Silva

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Abstract

We give a lightweight alternative construction of Jacobs's distributive law for multisets and distributions that does not involve any combinatorics. We first give a distributive law for lists and distributions, then apply a general theorem on 2-categories that allows properties of lists to be transferred automatically to multisets. The theorem states that equations between 2-cells are preserved by epic 2-natural transformations. In our application, the appropriate epic 2-natural transformation is defined in terms of the Parikh map, familiar from formal language theory, that takes a list to its multiset of elements.

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Dexter Kozen, Alexandra Silva. 2023-01-25. Multisets and Distributions. https://arxiv.org/abs/2301.10812

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