  We provide an algebraic formulation of C.Rovelli's relational quantum theory
that is based on suitable notions of "non-commutative" higher operator
categories, originally developed in the study of categorical non-commutative
geometry. As a way to implement C.Rovelli's original intuition on the
relational origin of space-time, in the context of our proposed algebraic
approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively
suggest to use this categorical formalism in order to spectrally reconstruct
non-commutative relational space-time geometries from categories of correlation
bimodules between operator algebras of observables. Parts of this work are
joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma),
Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok),
Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka
(Paris 13 University), Dr.Noppakhun Suthichitranont.
