Bérénice Delcroix-Oger (IRIF, Univ. Paris Diderot), Why operads can be seen as enhanced species and what they are used for.



Species have been introduced by Joyal in the 80s and are defined as functors (usually from the category of finite sets and bijections to itself), endowed with some operations. An operad can then be seen as a species enhanced with a natural transformation. After an explanation, with examples, of these definitions, I will give some examples illustrating the power of these notions, especially concerning freeness of algebras.