In
is given a “synthetic semantics” of a commutative strong monad TT. Where in the Lawvere-theory style semantics we have
“P∈T(X)P\in T(X) is an XX-ary operation on all TT-algebras (B,β)(B,\beta)
in synthetic (functional analysis) style this reads
“P∈T(X)P\in T(X) is an extensive quantity on XX”