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Multifunctorial inverse $K\mkern-2mu$-theory

Niles Johnson and Donald Yau

Vol. 7 (2022), No. 3, 507–548
Abstract

We show that Mandell’s inverse K-theory functor is a categorically enriched nonsymmetric multifunctor. In particular, it preserves algebraic structures parametrized by nonsymmetric operads. As applications, we describe how ring categories arise as the images of inverse K-theory.

Keywords
inverse $K\mkern-2mu$-theory, enriched multicategory, multifunctor, permutative category
Mathematical Subject Classification
Primary: 19D23
Secondary: 18D20, 18M05, 18M65, 55P43
Milestones
Received: 9 September 2021
Revised: 21 June 2022
Accepted: 15 July 2022
Published: 19 December 2022
Authors
Niles Johnson
Department of Mathematics
The Ohio State University at Newark
Newark, OH
United States
Donald Yau
Department of Mathematics
The Ohio State University at Newark
Newark, OH
United States