Lax algebra meets topology
Let \(\mathbb{T}\) be a monad on \(Set\), which extends to the category of sets and \(V\)-valued relations for a quantale \(V\). The examples of lax algebras for this type of monad include ordered sets, metric spaces, topological spaces, closure spaces, and approach spaces for suitable choices of \(V\) and \(\mathbb{T}\). In this paper, the authors present possible candidate axiomatisations for notions of `closed map' and `proper map' in such categories of lax algebras.
scientific article; zbMATH DE number 6047969
scientific article