  Pursuing the notions of ambidexterity and higher semiadditivity as developed
by Hopkins and Lurie, we prove that the span $\infty$-category of $m$-finite
spaces is the free $m$-semiadditive $\infty$-category generated by a single
object. Passing to presentable $\infty$-categories we obtain a description of
the free presentable $m$-semiadditive $\infty$-category in terms of a new
notion of $m$-commutative monoids, which can be described as spaces in which
families of points parameterized by $m$-finite spaces can be coherently summed.
Such an abstract summation procedure can be used to give a formal
$\infty$-categorical definition of the finite path integral described by Freed,
Hopkins, Lurie and Teleman in the context of 1-dimensional topological field
theories.
