Re: defining sets from abelian groups

In the Spring of 1971 at Chicago, Peter Freyd gave some very interesting lectures in which he showed how to construct a topos from a symmetric monoidal closed category by considering certain structured co-commutative co-algebras. This was done in such a way that for a group G one could recover the topos of G-sets (and hence the group itself) from the category of linear representations. Since the category of abelian groups has a unique closed monoidal structure, this should refute Vaughan Pratt's conjecture. It should have even many more applications than that, which is why I have long urged Peter to write it up. Bill Lawvere