Non-deterministic closure theory and universal arrows (Q5947272)

Motivated by the semantics of while-do commands for non-terminating and non-deterministic programming, the authors take the notion of closure operation of a partially ordered set \((U,\leq)\) (as an idempotent, monotone and extensive endofunction of \(U\)) to the context of a (thin) graph, where \(\leq\) is replaced by any relation \(R\) on \(U\) (keeping the idempotency requirement but interpreting monotonicity and extensiveness in terms of \(R\)), and characterize it in terms of so-called relational Moore families.