  This article aims to provide a novel formalization of the concept of
computational irreducibility in terms of the exactness of functorial
correspondence between a category of data structures and elementary
computations and a corresponding category of (1-dimensional) cobordisms. We
proceed to demonstrate that, by equipping both categories with a symmetric
monoidal structure and considering the case of higher-dimensional cobordism
categories, we obtain a natural extension of this formalism that serves also to
encompass non-deterministic or ``multiway'' computations, in which one
quantifies not only the irreducibility in the behavior of a single
(deterministic) computation path, but in the branching and merging behavior of
an entire ``multiway system'' of such paths too. We finally outline how, in the
most general case, the resulting symmetric monoidal functor may be considered
to be adjoint to the functor characterizing the Atiyah-Segal axiomatization of
a functorial quantum field theory. Thus, we conclude by arguing that the
irreducibility of (multi)computations may be thought of as being dual to the
locality of time evolution in functorial approaches to quantum mechanics and
quantum field theory. In the process, we propose an extension of the methods of
standard (monoidal) category theory, in which morphisms are effectively
equipped with intrinsic computational complexity data, together with an algebra
for how those complexities compose (both in sequence and in parallel, subject
to the monoidal structure).
