Information and Computation
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
Notions of computation and monads
Information and Computation
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Axiomatic domain theory in categories of partial maps
Axiomatic domain theory in categories of partial maps
Restriction categories I: categories of partial maps
Theoretical Computer Science
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Restriction categories II: partial map classification
Theoretical Computer Science - Category theory and computer science
Complete Cuboidal Sets in Axiomatic Domain Theory
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Complete Axioms for Categorical Fixed-Point Operators
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Restriction categories II: partial map classification
Theoretical Computer Science - Category theory and computer science
The HASCASL prologue: categorical syntax and semantics of the partial λ-calculus
Theoretical Computer Science
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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.