Algebras and view updates

Bob Rosebrugh – 11 March 2009

For the slice category C/V on a base category C with products, the sum functor sending X-->V to X is a left adjoint. Algebras for the generated monad are now called "lenses". They have appeared at least three times in theoretical computer science, most recently as "update strategies" for database views. When the base category is sets the lenses are "constant complement" strategies studied in the 1980's. For ordered sets as base, the more recent work of S. Hegner is recovered. We are currently studying lenses for categories, and will discuss recent results. This is joint work with Michael Johnson and Richard Wood.