Spahn extensive quantity

In

• Anders Kock, calculus of extensive quantity

is given a “synthetic semantics” of a commutative strong monad $T$. Where in the Lawvere-theory style semantics we have

“$P\in T(X)$ is an $X$-ary operation on all $T$-algebras $(B,\beta)$

in synthetic (functional analysis) style this reads

“$P\in T(X)$ is an extensive quantity on $X$”