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Multifunctorial K-Theory is an Equivalence of Homotopy Theories · arXivDesk

2205.08401May 17, 202220 pages. Final version. To appear in Journal of Homotopy and Related Structures

Multifunctorial $K$ -Theory is an Equivalence of Homotopy Theories

Niles Johnson, Donald Yau

Algebraic Topology Category Theory K-Theory and Homology

Abstract

We show that each of the three $K$ -theory multifunctors from small permutative categories to $\mathcal{G}_*$ -categories, $\mathcal{G}_*$ -simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these $K$

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We show that each of the three K-theory multifunctors from small permutative categories to G_*-categories, G_*-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these K-theory multifunctors, we describe an explicit homotopy inverse functor.

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Claims

The paper addresses: Multifunctorial K-Theory is an Equivalence of Homotopy Theories.
We show that each of the three K-theory multifunctors from small permutative categories to G_*-categories, G_*-simplicial sets, and connective spectra, is an equivalence of homotopy theories.

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Author comment: 20 pages. Final version. To appear in Journal of Homotopy and Related Structures