Dr. Emma Theart (Stellenbosch University) will give a seminar on Tuesday 8 July 2025 at 10:30 in the Sala Riunioni of the Department of Mathematics.
Title: Extensive morphisms
Abstract: Extensivity of a category can be described as a property of coproducts in the category, namely, that they are disjoint and universal. An alternative perspective is that it is a property of morphisms in a category. This talk explores this viewpoint by introducing natural notions of extensive and coextensive morphisms. A category is (co)extensive if and only if each morphism in the category is (co)extensive, but these notions also enable the study of (co)extensivity in categories where this property holds only for some morphisms. For instance while extensivity trivializes pointed categories, morphisms with trivial kernels in the category of pointed sets are still extensive. This approach also allows for categorical generalisations of concepts from universal algebra. The strict refinement property, which relates to unique factorisation, can be characterized by the coextensivity of product projections in the category. We examine various examples of (co)extensive morphisms and discuss the implications of (co)extensivity within certain classes of morphisms.
0 Comments