- - Date: Wed, 13 Mar 1996 19:30:06 GMT - From: Ralph Loader <loader@maths.ox.ac.uk> - ............................ - - Category theorists are keen on statements to the effect that structures are - defined by their universal properties. A typical book on topos theory may - define an elementary topos as a category with finite limits and power - objects. It then goes on to show that any topos has internal-homs. How? - By defining the function space as a certain set of sets of ordered pairs... ................................ - - Ralph. - - Nonsense. How can a set of sets of ordered pairs be an object of a topos. In fact, there is at least one book that defines a topos as a category with finite limits and power objects and constructs the internal homs as a limit of two arrows between two power objects. The construction is hidden inside a cotriple, but that is what it amounts to.