The theory of simultaneous equations
Tom Leinster ( University of Glasgow )
I will present a categorification of the elementary theory of linear simultaneous equations. Linear combinations become colimits. The idea, then, is that we have a family of objects, each described as a colimit of the others. From one point of view, this theory is about recursion (and I will say a few things about recursive type definitions). From another, it is about topology and self-similarity. Indeed, one of the first nontrivial examples of the theory is Freyd's coalgebraic characterization of the real interval, which I will explain.