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## The formal theory of theoriesAdd to your list(s) Download to your calendar using vCal - Nathanael Arkor (University of Cambridge)
- Friday 27 August 2021, 15:00-16:00
- https://meet.google.com/jxy-edcv-wgx.
If you have a question about this talk, please contact Nathanael Arkor. Since Linton’s remarkable insight that the algebraic theories of Lawvere are equivalent to monads on the category of sets, many correspondences of a similar nature have been discovered, leading to increasingly general theorems relating notions of theory to classes of monads. Most recently, the work of Lucyshyn-Wright and of Bourke–Garner establishes tight monad–theory correspondences in the setting of enriched categories. Despite the generality of these approaches, there are interesting examples that remain beyond reach, such as monads internal to topoi; graded monads; and Diers’s multimonads. More importantly, it is difficult to extract from the present approaches which assumptions are crucial to the monad–theory correspondence, and which arise simply as artefacts of the setting. Philosophically, we should like to know In this talk, I will outline a purely formal perspective on the monad–theory correspondence, working in the setting of a 2-category with a suitable factorisation system and having enough Kleisli objects. The motivating examples are given by the proarrow equipments of Wood admitting finite tight collages (that is, those satisfying Wood’s Axioms 4 and 5). It proves to be edifying first to establish a correspondence between theories and The first half of this talk concerns joint work with Dylan McDermott. This talk is part of the Logic & Semantics for Dummies series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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