Скачать или смотреть Edouard Balzin (Centre de Mathématiques Laurent Schwartz, École Polytechnique)

Title: Operation-indexing categories and Grothendieck fibrations

Abstract: It has been known since Segal that various small categories can
be used as blueprints for algebraic structures in homotopy theory,
providing alternatives to operads in such questions as for example delooping.The examples of those categories include finite sets, ordered sets, n-ordinals of Batanin and various exit path categories of configuration
spaces, as well as categories of operators of general topological operads.

We would like to offer a definition for such
operation-indexing categories, called weak operads or algebraic patterns,
and how to describe homotopy-algebraic structures over such things via
fibrations of model and higher categories. Depending on time and the
interest of the audience, we may attempt to introduce the notion of a
weak approximation as a means of establishing certain “Morita”-type
equivalences in the world of weak operads.