A bicategorical interpretation for relative Cuntz--Pimsner algebras

TL;DR

This paper provides a bicategorical framework for understanding relative Cuntz-Pimsner algebras, generalizing previous results on absolute cases by interpreting these constructions as reflectors in a correspondence bicategory.

Contribution

It introduces a bicategorical interpretation of relative Cuntz-Pimsner algebras, extending the categorical understanding from absolute to relative cases.

Findings

Generalizes previous characterizations of absolute Cuntz-Pimsner algebras

Provides a bicategorical perspective on relative Cuntz-Pimsner algebras

Shows these algebras as reflectors in a sub-bicategory

Abstract

We interpret the construction of relative Cuntz-Pimsner algebras of correspondences in terms of the correspondence bicategory, as a reflector into a certain sub-bicategory. This generalises a previous characterisation of absolute Cuntz-Pimsner algebras of proper correspondences as colimits in the correspondence bicategory.