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Gabriel-Ulmer duality and Lawvere theories enriched over a general base


Reference:

Lack, S. and Power, J., 2009. Gabriel-Ulmer duality and Lawvere theories enriched over a general base. Journal of Functional Programming, 19 (3-4), pp. 265-286.

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    Official URL:

    http://dx.doi.org/10.1017/s0956796809007254

    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 all 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.

    Details

    Item Type Articles
    CreatorsLack, S.and Power, J.
    DOI10.1017/s0956796809007254
    DepartmentsFaculty of Science > Computer Science
    Publisher StatementPower_JFP_2009_19_3-4_265.pdf: © 2009 Cambridge University Press
    RefereedYes
    StatusPublished
    ID Code14889

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