## Commutative or monoidal monadsAdd to your list(s) Download to your calendar using vCal - Paul Taylor (U of Brum (honorary))
- Thursday 13 July 2017, 12:00-13:00
- CS 217.
If you have a question about this talk, please contact Dr Steve Vickers. The purpose of this talk is to ask the audience’s help in understanding the title. Steve Vickers and I are working towards the notion of colocale, but coming to it from completely different directions. My approach is from pure category theory, asking what interesting things you can say about adjunctions that are both monadic and comonadic. Limits of algebras are easy, as are colimits of coalgebras, but after making both steps you’re lost. However, the category of coalgebras over algebras has binary products so long as the original category has them and the monad has a strength. This by-passes consideration of the algebras alone, but in the spirit of treating both ends of the adjunction with equal importance, we should find out what is going on there. Unwinding my construction of products of coalgebras, we get tensor products of algebras, but only under additional hypotheses. The notion of strength of a monad is manifestly asymmetrical. Rectifying this gives a commutative monad. In the concrete direction, I think that commutative monads correspond to algebraic theories that are commutative in the sense that every operation symbol commutes with every other and so a homomoprhism. More abstractly, a commutative monad is apparently the same as a monadic monad. This construction yields the familiar tensor products of vector spaces and of complete semilattices, so the ideas are familiar in several disciplines. This talk is part of the Lab Lunch series. ## This talk is included in these lists:- CS 217
- Computer Science Departmental Series
- Computer Science Distinguished Seminars
- Lab Lunch
- Theoretical computer science seminar
- computer sience
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## Other listsAnalysis Reading Seminar 2019/2020 IMA West Midlands Branch Midlands Logic Seminar## Other talksTBC |