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Co-authored-by: Fredrik Bakke <[email protected]>
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lowasser and fredrik-bakke authored Feb 10, 2025
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## Idea

For two [subsets](group-theory.subsets-commutative-monoids.md) `A`, `B` of a
[commutative monoid](group-theory.commutative-monoids.md) `M`, the Minkowski
multiplication of `A` and `B` is the set of elements that can be formed by
multiplying an element of `A` and an element of `B`. (This is more usually
referred to as a Minkowski sum, but as the operation on commutative monoids is
referred to as `mul`, we use multiplicative terminology.)
Given two [subsets](group-theory.subsets-commutative-monoids.md) `A` and `B` of a
[commutative monoid](group-theory.commutative-monoids.md) `M`, the {{#concept "Minkowski multiplication" Disambiguation="on subsets of a commutative monoid" WD="Minkowski addition" WDID=Q1322294 Agda=minkowski-mul-Commutative-Monoid}} of `A` and `B` is the [set](foundation-core.sets.md) of elements that can be formed by
multiplying an element of `A` and an element of `B`. This binary operation defines a commutative monoid structure on the [powerset](foundation.powersets.md) of `M`.

## Definition

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