Paracategories. I: Internal paracategories and saturated partial algebras (Q1884899)

A paracategory is a set with partial \(n\)-ary operations behaving like the composition operations in a subset of the set of morphisms in a category. The authors give an alternative axiomatisation based on the category of finite ordinals, which makes sense in any bicategory of partial maps. More generally, they consider partial algebras over monads. A partial algebra has an enveloping algebra, analogous to the enveloping category of a paracategory, but in the more general theory it is not always possible to recover a partial algebra from its enveloping algebra. Partial algebras for which this is possible are called saturated.