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.
Email your librarian or administrator to recommend adding this journal to your organisation's collection.
* Views captured on Cambridge Core between September 2016 - 23rd May 2017. This data will be updated every 24 hours.