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

Professor Bart Jacobs ( Radboud University Nijmegen )

- 14:00 23rd April 2010 ( week 0th week, Trinity Term 2010 )Lecture Theatre B, Computing Laboratory

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.

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.