Michael Ching

Title: Day convolution, infinity-operads and Goodwillie calculus (slides)
Abstract: Goodwillie calculus is a branch of homotopy theory that provides systematic approximations to a suitable functor (say from the category of topological spaces to itself) in the form of a “Taylor tower”, analogous to the Taylor series from ordinary calculus. In this talk, I will describe how some aspects of the Taylor tower construction are related via Day convolution. The slogan will be that “the nth derivative is an n-fold Day convolution of the first derivative”.
An important consequence of this observation is that the derivatives of an identity functor on a category C are a coloured operad (or symmetric multicategory), with the derivatives of a functor from C to D forming a bimodule over the operads corresponding to C and D. The context for all of this work is Lurie’s theory of infinity-categories though no technical background from that theory will be required in this talk.