Chu spaces as a semantic bridge between linear logic and mathematics. (Q1398475)

The author has for some time been a strong advocate of the usefulness of categories of Chu spaces in both pure mathematics and theoretical computer science. In the present paper, he gives a brief but clear overview of the constructions and basic properties of the `big' and `little' Chu categories \(\mathcal{C}hu (\mathcal{S}et,\Sigma)\) and \(chu(\mathcal{S}et,\Sigma)\). He then shows how they may be used for modelling linear logic, and also describes how arbitrary small categories may be concretely embedded in \(\mathcal{C}hu (\mathcal{S}et,\Sigma)\) for suitable \(\Sigma\). His thesis is that linear logic is `the categorical logic of general mathematics', just as intuitionistic categorical logic is `the categorical logic of cartesian closed mathematics', and that just as \(\mathcal{S}et\) is the `exemplar category' of the latter, so \(\mathcal{C}hu (\mathcal {S}et,-)\) is the exemplar category of general mathematics.