An absolute characterisation of locally determined omega-colimits

TL;DR

This paper provides a universal characterization of locally determined omega-colimits using omega-cocontinuity of locally continuous functors, with a proof leveraging the enriched Yoneda embedding, applicable to recursive domain equations.

Contribution

It introduces a universal characterization of locally determined omega-colimits via omega-cocontinuity, extending to locality notions for adjoint pairs.

Findings

Universal characterization of omega-colimits established

Proof utilizes enriched Yoneda embedding

Generalization to locality for adjoint pairs

Abstract

Characterising colimiting omega-cocones of projection pairs in terms of least upper bounds of their embeddings and projections is important to the solution of recursive domain equations. We present a universal characterisation of this local property as omega-cocontinuity of locally continuous functors. We present a straightforward proof using the enriched Yoneda embedding. The proof can be generalised to Cattani and Fiore's notion of locality for adjoint pairs.