Full title: A point-free approach to fundamental groups: the Kennison fundamental pro-group of a connected and locally connected locale
Speaker: Jean Paul Schemeil – University of Nottingham
Abstract: The aim of this talk is to introduce the notions of the fundamental pro-sheaf and pro-group of locales, first introduced by John F. Kennison in “What is the fundamental group?” (Journal of Pure and Applied Algebra, 1989). We will review some foundational aspects of locale theory, motivating how locales can be correctly thought as “pointless” topological spaces. The central focus of the talk is the presentation of a conjecture that aims to generalise the classical Seifert-Van Kampen theorem to the Kennison fundamental pro-group of pointed, connected, and locally connected locales. Along with a discussion of some positive partial results, we will also highlight potential areas for further investigation.