Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bicategories of C*-correspondences as Dwyer-Kan localisations

Ralf Meyer

Abstract

We show that the bicategory of proper correspondences is the Dwyer-Kan localisation of the category of C*-algebras at a certain class of *-homomorphisms.

Bicategories of C*-correspondences as Dwyer-Kan localisations

Abstract

We show that the bicategory of proper correspondences is the Dwyer-Kan localisation of the category of C*-algebras at a certain class of *-homomorphisms.

Paper Structure

This paper contains 5 sections, 6 theorems, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The nerve of the proper correspondence bicategory
  3. C*-stable functors
  4. Proof of the main theorem
  5. Some variants of the main theorem

Key Result

Lemma 3.3

A functor on the category of $\sigma$-unital $\mathrm C^*$-algebras is $\mathrm C^*$-stable if and only if it maps the special corner embeddings $B\to \mathbb K(\ell^2\mathbb N)\otimes B$, $b\mapsto E_{00} \otimes b$, to equivalences.

Figures (1)

  • Figure 1: The simplicial sets that occur in the construction for $n=2$

Theorems & Definitions (12)

  • Definition 2.1
  • Definition 3.1
  • Example 3.2
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • Proposition 4.1
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • ...and 2 more