Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

A lax monoidal model for multilinearization

Pages: 319 – 331

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a18


Sarah Yeakel (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)


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

Copyright © 2019, Sarah Yeakel. Permission to copy for private use granted.

Received 1 September 2018

Received revised 25 June 2019

Accepted 9 July 2019

Published 11 December 2019