  The goal of this work is twofold: (i) to provide a detailed analysis of some
categories of inductive graded ring - a concept introduced in [DM98] in order
to provide a solution of Marshall's signature conjecture in the algebraic
theory of quadratic forms; (ii) apply this analysis to deepen the connections
between the category of special hyperfields ([dARM22]) - equivalent to the
category of special groups ([DM00]) and the categories of inductive graded
rings.
