Gabriel–ulmer duality and lawvere theories enriched over a general base

Authors:
Stephen Lack;John Power
Affiliations:
School of computing and mathematics, university of western sydney, locked bag 1797, penrith south dc, nsw 1797, australia (e-mail: s.lack@uws.edu.au);Department of computer science, university of bath, claverton down, bath ba2 7ay, uk (e-mail: a.j.power@bath.ac.uk)
Venue:
Journal of Functional Programming
Year:
2009

Citing 13
Cited 0

Computational lambda-calculus and monads

Proceedings of the Fourth Annual Symposium on Logic in computer science
Category theory for computing science

Category theory for computing science
Notions of computation and monads

Information and Computation
Why tricategories?

Information and Computation
ALGOL-like languages (v.2)

ALGOL-like languages (v.2)
Notions of Computation Determine Monads

FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Monads and Modularity

FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Monads and Effects

Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Probabilistic Domains

CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Combining effects: sum and tensor

Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Discrete Lawvere theories and computational effects

Theoretical Computer Science - Algebra and coalgebra in computer science
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads

Electronic Notes in Theoretical Computer Science (ENTCS)
Combining algebraic effects with continuations

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

Motivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads on Set. We generalise that relationship from Set to an arbitrary locally presentable category such as Poset and ωCpo or functor categories such as [Inj, Set] and [Inj, ωCpo]. That involves allowing the arities of Lawvere theories to be extended to being size-restricted objects of the locally presentable category. We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel–Ulmer duality.