Apparaît dans la collection : Summer School 2026 - ICRA 2026

This is an introductory course on infinity-categories. Over the first two lectures, we will define quasi-categories, the concepts of limit, colimit and localisation. The aim is to present quasi-categories as a natural concept at the interface between categories and topological spaces through the lens of simplicial sets and to understand the notion of equivalence between quasi-categories. The aim is to understand statements that use infinity-categories, whilst trying to be as non-technical as possible. The content of the third lecture will depend on the time available. The aim, however, is to briefly discuss other models of infinity-categories, to explain why there is an infinity-category underlying a DG category and, time permitting, to introduce stable infinity-categories. The first two lectures will draw mainly on Cisinski’s book “Higher categories and homotopical algebra”.