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. For each of these K -theory multifunctors, we describe an explicit homotopy inverse functor. As a separat...

Full description

Saved in:
Bibliographic Details
Published in:Journal of homotopy and related structures 2022-12, Vol.17 (4), p.569-592
Main Authors: Johnson, Niles, Yau, Donald
Format: Article
Language:English
Subjects:
Algebra
Algebraic Topology
Categories
Equivalence
Functional Analysis
Homotopy theory
Mathematics
Mathematics and Statistics
Number Theory
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann–Osorno E ∗ -categories is equivalent to the homotopy theory of pointed simplicial categories.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-022-00317-8