Local reflections between relations, spans and polynomials

Charles Walker – 2 December 2015

Given a locally cartesian closed regular category E, we may form the bicategories of relations, spans and polynomials. In this talk, we will first use the local reflections between the bicategories of relations and spans to derive the universal property of relations from that of spans. We will then proceed by proving our main result: that the inclusion of spans into polynomials has a right adjoint in the 2-category of bicategories, lax functors and icons; which exhibits Span(E) as a locally coreflective sub-bicategory of Poly(E).