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Paracategories I: internal paracategories and saturated partial algebras

Authors
Journal
Theoretical Computer Science
0304-3975
Publisher
Elsevier
Publication Date
Volume
309
Identifiers
DOI: 10.1016/s0304-3975(03)00135-x
Keywords
  • Partialt-Algebras
  • Monoid Classifier
  • Paracetegories
  • Saturation
Disciplines
  • Mathematics

Abstract

Abstract Based on the monoid classifier Δ, 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.

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