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University of Cambridge > Talks.cam > Logic and Semantics Seminar (Computer Laboratory) > Scalars & probabilities, monads & categories

## Scalars & probabilities, monads & categoriesAdd to your list(s) Download to your calendar using vCal - Bart Jacobs, Radboud University Nijmegen, The Netherlands
- Friday 21 May 2010, 14:00-15:00
- Room FW11, Computer Laboratory, William Gates Building.
If you have a question about this talk, please contact Sam Staton. The talk consist of two separate but connected parts. The first part is joint work with Dion Coumans (Nijmegen). It describes interrelatedness between: - algebraic structure on sets of scalars,
- properties of monads associated with such sets of scalars, and
- structure in categories (esp. Lawvere theories) associated with these monads.
These interrelations will be expressed in terms of ``triangles of adjunctions’’, involving for instance various kinds of monoids (non-commutative, commutative, involutive) and semirings as scalars. It will be shown to which kind of monads and categories these algebraic structures correspond via adjunctions. The second part will investigate extensions of these results to probabilities as scalars. It involves convex sets, effect algebras, and a new class of functors that we call `convex functors’; they include what are usually called probablity distribution functors. The relationships take the form of three adjunctions. Two of these three are `dual’ adjunctions for convex sets, one time with the Boolean truth values {0,1} as dualising object, and one time with the probablity values [0,1] of the unit interval. The third one is a new adjunction between effect algebras and convex functors, forming the first step towards a ``triangle of adjunctions’’ in this probabilistic area. This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series. ## This talk is included in these lists:- All Talks (aka the CURE list)
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## Other listsGates Cambridge Annual Lecture EPRG Energy and Environment (E&E) Series Easter 2012 Associative experiment## Other talks***PLEASE NOTE THIS SEMINAR IS CANCELLED*** Translational Science: using biomarkers to guide clinical development in oncology Improving on Nature: Biotechnology and the Ethics of Animal Enhancement Adding turbulent convection to geostrophic circulation: insights into ocean heat transport Identification of Active Species and Mechanistic Pathways in the Enantioselective Catalysis with 3d Transition Metal Pincer Complexes Are hospital admissions for people with palliative care needs avoidable and unwanted? Cambridge-Lausanne Workshop 2018 - Day 1 Protein Folding, Evolution and Interactions Symposium Black and British Migration 'Politics in Uncertain Times: What will the world look like in 2050 and how do you know? Synthetic Cellularity via Protocell Design of Soft Matter Interfaces |