09/11/2007 - 16:00

Speaker:

Michael Barr

Location:

Room 920, Burnside Hall, McGill University

Abstract:

An Isbell duality arises when the "same" object lives in two different categories. Examples abound, often when the object is 2. We attempt to flesh out this concept of an object in two categories. We give one new example that leads to a duality between totally disconnected Tychonoff (completely regular hausdorff) spaces and a class of subrings of powers of Z. In this case, Z is the object in question. We show how this applies to the known dualities between all Tychonoff spaces and a class of subrings of powers of R as well as to the classical Isbell duality between sober spaces and powers of the Sierpinski space.

Joint work with John Kennison and Robert Raphael.