A note on noncommutative CW-spectra

TL;DR

This paper provides an alternative proof that the category of noncommutative CW-spectra can be modeled as spectral presheaves on a category of suspension spectra of matrix algebras, using well-known model category results.

Contribution

It offers a new proof of a key result in noncommutative CW-spectra theory, simplifying the original proof by leveraging established model category techniques.

Findings

Category of noncommutative CW-spectra is equivalent to spectral presheaves on a specific category M.

Objects in M are interpreted as suspension spectra of matrix algebras.

The proof relies on well-known results in stable model categories.

Abstract

We use the machinery of arXiv:2009.07539 to give an alternative proof of one of the main results of arXiv:2101.09775. This result states that the category of noncommutative CW-spectra can be modelled as the category of spectral presheaves on a certain category M, whose objects can be thought of as "suspension spectra of matrix algebras". The advantage of our proof is that it mainly relies on well-known results on (stable) model categories.