Restriction for Semigroups and Categories First afternoon talk of Calgary workshop

Restriction for Semigroups and Categories First afternoon talk of Calgary workshop Ernie Manes, June 2, 2006 This handout includes axiom systems useful for the talk, a very small set of definitions in category theory and a 12-step program to help semigroup theorists who have never studied category theory to get up to speed. The references at the end will be mentioned in the talk. Slogan: In the study of semigroups, it is sometimes useful to add some new objects to obtain a category associated with that semigroup. Tentative talk outline: 1. History of restriction in semigroups. 2. The unusual expressiveness of universal mapping properties. 3. Idempotents: monoids vs. categories. 4. The regular representation is the Yoneda embedding. 5. Boolean restriction.