Our motivating interest in Chu spaces has been as a universal model of computation. More recently and to our considerable surprise, we have found that every algebraic and/or topological object of mathematics is representable as a Chu space, in such a way that the above transformations are in one-to-one correspondence with those functions that are homomorphisms and/or continuous when definable traditionally. Restating this in categorical language, the many diverse categories of mathematics all embed fully and concretely in different regions of the one category of Chu spaces, whose objects may then be understood as spanning the gamut from sets as the most discrete objects of mathematics to complete atomic Boolean algebras, aka antisets, as the most coherent.
There being no explicit notion of either signature or theory here, this implies that every Chu space must come with both signature and theory built in implicitly, along with the ability to communicate appropriately with objects having both similar and dissimilar signatures. The talk will focus on explaining how such an unsophisticated mechanism can exhibit such sophisticated behavior.
This is the final speaker in the Distinguished Lecturer Series of the DIMACS Special Year on Logic and Algorithms.
For additional information about the DIMACS special year, please see the following web site: