Gabriel-Ulmer duality and Lawvere theories enriched over a general base | Macquarie University ResearchOnline

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Title: Gabriel-Ulmer duality and Lawvere theories enriched over a general base
Related: Journal of functional programming, Vol. 19, Issue 3-4, (2009), p.265-286
DOI: 10.1017/S0956796809007254
Publisher: Cambridge University Press
Date: 2009
FoR/RFCD Code(s): 080300 Computer Software 010300 Numerical and Computational Mathematics 010200 Applied Mathematics
Author/Creator: Lack, Stephen
Author/Creator: Power, John
Description: 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.
Description: 22 page(s)
Subject Keyword: 080300 Computer Software
Subject Keyword: 010300 Numerical and Computational Mathematics
Subject Keyword: 010200 Applied Mathematics
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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