Dipartimetno di Matematica, Aula Seminari.
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.
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