# A Monoidal Model for Goodwillie Derivatives

Research paper by Sarah Yeakel

Indexed on: 21 Jun '17Published on: 21 Jun '17Published in: arXiv - Mathematics - Algebraic Topology

#### Abstract

Using the category of finite sets and injections, we construct a lax monoidal model for Goodwillie's derivatives of a functor between spaces or spectra. Along the way, we show that the cross effects of a monad form a functor-operad. We also recover a chain rule for endofunctors of spaces, expressing the derivatives of the composite \$F \circ G\$ as a derived composition product of the derivatives of \$F\$ and \$G\$.