Information and Computation
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Lifting Theorems for Kleisli Categories
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
Restriction categories II: partial map classification
Theoretical Computer Science - Category theory and computer science
An equational notion of lifting monad
Theoretical Computer Science - Category theory and computer science
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
Boolean restriction categories and taut monads
Theoretical Computer Science
Taut Monads, Dynamic Logic and Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
Restriction categories III: colimits, partial limits and extensivity
Mathematical Structures in Computer Science
Boolean and classical restriction categories
Mathematical Structures in Computer Science
Unitary Theories, Unitary Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
Timed Sets, Functional Complexity, and Computability
Electronic Notes in Theoretical Computer Science (ENTCS)
Restriction categories as enriched categories
Theoretical Computer Science
Hi-index | 5.23 |
Given a category with a stable system of monics, one can form the corresponding category of partial maps. To each map in this category there is, on the domain of the map, an associated idempotent, which measures the degree of partiality. This structure is captured abstractly by the notion of a restriction category, in which every arrow is required to have such an associated idempotent. Categories with a stable system of monics, functors preserving this structure, and natural transformations which are cartesian with respect to the chosen monics, form a 2-category which we call MCat. The construction of categories of partial maps provides a 2-functor Par:Mcat→Cat. We show that Par can be made into an equivalence of 2-categories between MCat and a 2-category of restriction categories. The underlying ordinary functor Par&r0:Mcat&0 → Ca t0 of the above 2-functor Par turns out to be monadic, and, from this, we deduce the completeness and cocompleteness of the 2-categories of M-categories and of restriction categories. We also consider the problem of how to turn a formal system of subobjects into an actual system of subobjects. A formal system of subobjects is given by a functor into the category sLat of semilattices. This structure gives rise to a restriction category which, via the above equivalence of 2-categories, gives an M-category. This M-category contains the universal realization of the given formal subobjects as actual subobjects.