  A categorical point of view about minimization in subrecursive classes is
presented by extending the concept of Symmetric Monoidal Comprehension to that
of Distributive Minimization Comprehension. This is achieved by endowing the
former with coproducts and a finality condition for coalgebras over the
endofunctor sending X to ${1}\oplus{X}$ to perform a safe minimization
operator. By relying on the characterization given by Bellantoni, a tiered
structure is presented from which one can obtain the levels of the Polytime
Hierarchy as those classes of partial functions obtained after a certain number
of minimizations.
