  We prove that the category $\mathsf{SBor}$ of standard Borel spaces is the
(bi-)initial object in the 2-category of countably complete Boolean (countably)
extensive categories. This means that $\mathsf{SBor}$ is the universal category
admitting some familiar algebraic operations of countable arity (e.g.,
countable products, unions) obeying some simple compatibility conditions (e.g.,
products distribute over disjoint unions). More generally, for any infinite
regular cardinal $\kappa$, the dual of the category
$\kappa\mathsf{Bool}_\kappa$ of $\kappa$-presented $\kappa$-complete Boolean
algebras is (bi-)initial in the 2-category of $\kappa$-complete Boolean
($\kappa$-)extensive categories.
