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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.



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