Relational presheaves, change of base and weak simulation

We show that considering labelled transition systems as relational presheaves captures several recently studied examples in a general setting. This approach takes into account possible algebraic structure on labels. We show that left (2-)adjoints to change-of-base functors between categories of relational presheaves with relational morphisms always exist and, as an application, that weak closure (in the sense of Milner) of a labelled transition system can be understood as a left adjoint to a change-of-base functor.