Infinity-categories and infinity-operads

by Francesca Pratali (Université Sorbonne Paris Nord)

Thursday 3 Nov 2022, 11:00 → 12:00 Europe/Rome

Aula Seminari (Dipartimetno di Matematica)

An operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs and one output, as well as maps defining composition laws. A coloured operad is an operad where input elements and the output are allowed to have a specific  type; one can regard an ordinary category as a coloured operad whose operations are only those with one input.

In this talk, I will present the constructions of different models for homotopy-coherent notions of category and operad, namely infinity-categories and infinity-operads, and I will give an account of the relation between them in terms of Quillen model categories. I will focus on some result of equivalences and expose some of the applications of this theory.