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Scalars, Monads, and Categories (and maybe a bit more)

Professor Bart Jacobs ( Radboud University Nijmegen )
Interrelatedness will be described between: (1) algebraic
structure on sets of scalars, (2) properties of monads associated
with such sets of scalars, and (3) 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.

Time permitting, as appendix to this part, some recent
work relating to a functorial approach to quantum computing
and measurement will be described.

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