7 March 2018, Algebra|Coalgebra Seminar, Benno van den Berg

The purpose of this talk is to introduce the notion of a path category (short for a category with path objects). Like other notions from homotopical algebra, such as a category of fibrant objects or a Quillen model structure, it provides a setting in which one can develop some homotopy theory. For a logician this type of category is interesting because it provides a setting in which many of the key concepts of homotopy type theory (HoTT) make sense. Indeed, path categories provide a syntax-free way of entering the world of HoTT, and familiarity with (the syntax of) type theory will not be assumed in this talk. Instead, I will concentrate on basic examples and results. (This is partly based on joint work with Ieke Moerdijk.)