# Bicategories of C*-correspondences as Dwyer-Kan localisations

## TL;DR

This paper demonstrates that the bicategory of proper correspondences can be obtained by localizing the category of C*-algebras at specific *-homomorphisms, providing a new perspective on their structure.

## Contribution

It establishes that the bicategory of proper correspondences is the Dwyer-Kan localization of the category of C*-algebras at a particular class of *-homomorphisms, linking bicategorical and categorical localizations.

## Key findings

- Bicategory of proper correspondences is a Dwyer-Kan localization.
- Identifies the class of *-homomorphisms used for localization.
- Provides a new categorical framework for C*-algebras.

## 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.