A Monoidal Model for Multilinearization

Abstract

Using the category of finite sets and injections, we construct a new model for the multilinearization of multifunctors between spaces that appears in the derivatives of Goodwillie calculus. We show that this model yields a lax monoidal functor from the category of symmetric functor sequences to the category of symmetric sequences of spaces after evaluating at the unit.

Significantly rewritten after mistake found in proof that cross effects form a functor-operad

Cited by in corpus (3)

• On the Goodwillie derivatives of the identity in structured ring spectra
• Infinity-operads and Day convolution in Goodwillie calculus
• The partition poset complex and the Goodwillie derivatives of the identity in spaces