On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras

TL;DR

This paper develops a unified approach to globalizing partial actions and coactions across sets, topological spaces, and algebras, extending known results and enabling new applications.

Contribution

It applies the theory of geometric partial comodules to unify and extend the globalization of partial actions and coactions in various categories.

Findings

Unified framework for globalization of partial actions and coactions

Recovery of all known results in the studied settings

Extension to new cases of interest

Abstract

We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We show that this approach does not only allow to recover all known results in these settings, but it allows to treat new cases of interest, too.