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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 $G$.