Paracategories II: adjunctions, fibrations and examples from probabilistic automata theory

摘要

In this sequel to Hermida and Mateus (Paracategories I: internal paracategories and saturated partial algebras, Theoret. Comput. Sci., in press), we explore some of the global aspects of the category of paracategories. We establish its (co) completeness and cartesian closure. From the closed structure we derive the relevant notion of transformation for paracategories. We set up the relevant notion of adjunction between paracategories and apply it to define (co) completeness and cartesian closure, exemplified by the paracategory of bivariant functors and dinatural transformations. We introduce partial multicategories to account for partial tensor products. We also consider fibrations for paracategories and their indexed-paracategory version. Finally, we instantiate all these concepts in the context of probabilistic automata.