Name
Abstract | ||
|---|---|---|
We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus, equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers. The representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads. It is proved using a direct axiomatization of Kleisli categories of equational lifting monads. This axiomatization is of interest in its own right. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0304-3975(01)00243-2 | Theor. Comput. Sci. |
Keywords | DocType | Volume |
partial map,equational notion,commutative strong monad,equational lifting,Commutative strong monads,representation theorem,Categories,Kleisli category,equational lifting monad,Abstract Kleisli,partial category,equational property,direct axiomatization,partial map classifier,Partiality and partial categories,Premonoidal categories | Journal | 294 |
Issue | ISSN | Citations |
1-2 | Theoretical Computer Science | 3 |
PageRank | References | Authors |
0.55 | 9 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anna Bucalo | 1 | 39 | 4.12 |
| Carsten Führmann | 2 | 31 | 3.50 |
| Alex Simpson | 3 | 113 | 14.15 |