Shannon entropy is a powerful concept. But what properties single out
Shannon entropy as special? Instead of focusing on the entropy of a
probability measure on a finite set, it can help to focus on the
"information loss", or change in entropy, associated with a
measure-preserving function. Shannon entropy then gives the only
concept of information loss that is functorial, convex-linear and
continuous. This is joint work with Tom Leinster and Tobias Fritz.