Title: “From algebraic topology to algebraic set theory”

Course description: In the first two lectures, we will discuss several approaches to axiomatic homotopy theory (notably Brown’s Categories of Fibrant Objects and  Quillen’s Model Categories). We will then present a categorical axiomatisation of set theory, in the style of Algebraic Set Theory but directed more towards models of predicative set theory. In a final lecture, we will discuss how one can pass from (models of) the first axiomatisation to the second one. (This last part is based on joint work with Benno van den Berg).