A lax monoidal model for multilinearization

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 $S^0$. We also give a construction which extends the result to symmetric sequences of spectra.

2010 Mathematics Subject Classification

18D50, 55P47, 55P65

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Received 1 September 2018

Received revised 25 June 2019

Accepted 9 July 2019

Published 11 December 2019