## Paracategories I: Internal Paracategories and Saturated Partial Algebras (2002)

Venue: | Comp. Sci |

Citations: | 5 - 1 self |

### BibTeX

@ARTICLE{Hermida02paracategoriesi:,

author = {Claudio Hermida and Paulo Mateus},

title = {Paracategories I: Internal Paracategories and Saturated Partial Algebras},

journal = {Comp. Sci},

year = {2002},

volume = {309},

pages = {125--156}

}

### OpenURL

### Abstract

Based on the monoid classi er , 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 inclusions and Kleene morphisms.

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