Let $S$ be a semigroup on which acts $\mathbb{R}_{\geq0}$. Does this structure has a name?
For example $S$ can be the set of convex bodies in $\mathbb{R}^n$ with the Minkowsky sum.
2026-03-28 00:47:41.1774658861
Terminology for a weaked vector space
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Assuming you want the semigroup to be commutative (as it is for Minkowski sum), such an object is called a convex cone.
Added: When if it's not naturally sitting in a vector space, one can avoid confusion by calling the object an abstract convex cone. For example, Wikipedia talks about