Paracategories I: internal paracategories and saturated partial algebras

✍ Scribed by Claudio Hermida; Paulo Mateus

• Book ID: 104325803
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 796 KB
• Volume: 309
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(03)00135-x

✦ Synopsis

Based on the monoid classiÿer , we give an alternative axiomatization of Freyd's paracategories, which can be interpreted in any bicategory of partial maps. Assuming furthermore a free-monoid monad T in our ambient category, and coequalisers satisfying some exactness conditions, we give an abstract envelope construction, putting paramonoids (and paracategories) in the more general context of partial algebras. We introduce for the latter the crucial notion of saturation, which characterises those partial algebras which are isomorphic to the ones obtained from their enveloping algebras. We also set up a factorisation system for partial algebras, via epimorphisms and (monic) Kleene morphisms and relate the latter to saturation.