11 September 2007 
4:00 - 5:00   Michael Barr

25 September 2007 
4:00 - 5:00   Michael Barr


Authors: Michael Barr, John Kennison, Robert Raphael
Title: Isbell duality


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.