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Title:An equational notion of lifting monad
Authors: Anna Bucalo ; Carsten Fuhrmann ; Alexander Simpson
Date: 2003
Publication Title:Theoretical Computer Science
Publication Type:Journal Article Publication Status:Published
Volume No:294 Page Nos:31-60
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 non-equational 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.
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Bibtex format
author = { Anna Bucalo and Carsten Fuhrmann and Alexander Simpson },
title = {An equational notion of lifting monad},
journal = {Theoretical Computer Science},
publisher = {Elsevier},
year = 2003,
volume = {294},
pages = {31-60},
doi = {10.1016/S0304-3975(01)00243-2},

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