Dear all, In "Categories for the Working Mathematician", Mac Lane gives a nice argument that the monoidal category of sets, taken with cartesian product as tensor product, is not monoidally equivalent to a strict skeletal monoidal category. (He attributes this argument to Isbell.) He also claims that this argument extends to the category of abelian groups, with monoidal operation given by tensor product. Could someone spell this out for me? I'm particularly interested in showing that vector spaces with dimensions bounded by some infinite cardinality cannot form a monoidal category equivalent to a strict, skeletal one. I expect the techniques used for the abelian group case would also apply here. Best wishes, Jamie. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]