Tensor product of partial acts
Keywords:Partial action, Partial act, partial biact, tensor product, adjoint functors
In this article we define the tensor product of partial acts over a semigroup and prove several properties of this tensor product. We also define the notion of a polite partial biact, which is needed to define partial actions on the tensor product of partial acts. Finally, we prove that a certain tensor functor of partial acts is left adjoint of a certain hom-functor of partial acts.