Goodwillie calculus in the category of algebras over a chain operad

Abstract

Goodwillie functor calculus is a method invented by Thomas Goodwillie to analyze functors that arise in Topology. This theory has some compelling similarities with differential calculus of Newton and Leibnitz in the sense that the method produces a tower for approximating a functor which plays the role of the Taylor series approximating a function. One of the major difficulties in this theory is that, Goodwillie Taylor series (or towers) are very abstract from their constructions and hence not easy to compute in general. The goal of this thesis is to produce an explicit approximation of functors between algebraic categories. Namely, we look at functors between the category of chain complexes and the category of algebras over a chain complex operad. We study properties on their tower of approximation, such as analyzing the difference between two consecutive terms of the Taylor tower. Moreover, we extend this approach to produce an explicit and computable description of the Taylor tower.(SC - Sciences) -- UCL, 202