I was unable to understand John Baez' golden object problem, nor his description of the solutions. He refuses to tell us what 'nice' means, but let me at least propose that to be 'tolerable' a solution must be an object in a category, and John doesn't tell us what category is involved in either of the solutions; at least I couldn't find a specification of the objects, nor the maps, so I found the descriptions 'intolerable', in the technical sense defined above. He is very generous, allowing one to use a category with both plus and times as extra monoidal structures. (Does anyone know an example of interest in which the plus is not coproduct?) This freedom is unnecessary; a little algebra plus Robbie Gates' theorem provides a solution G to G^2additional equations, in an extensive category (with coproduct as plus, cartesian product as times). Briefly, here it is. A primitive fifth root of unity z is a root of the polynomial 1+X+X^2+X^3+X^4, hence satisfies 1+z+z^2+z^3+z^4+zwhich is of the 'fixed point' form p(z)0. Gates' theorem then says that the free distributive category containing an object Z and an isomorphism from p(Z) to Z is extensive, and its Burnside rig B (of isomorphism classes of objects) is, as one would hope, N[X]/(p(X)equations. Since the degree of p is greater than 1, an easy general theorem tells us (from the joint injectivity of the Euler and dimension homomorphisms) that two polynomials agree at the object Z if and only if either they are the same polynomial or both are non-constant and they agree at the number z.Now the 'algebra': the golden number is 1+z+z^4. So G satisfies G^2unexpected equations, because the relation X^2polynomial in N[X] to a linear polynomial, and these reduced forms have distinct Euler characteristics, i.e. differ at z. Thus the homomorphism from N[X]/(X^2I wanted. Since in the category of sets, any nasty old infinite set satisfies the golden equation and many others, I have taken the liberty of interpreting 'nice' to mean at least 'satisfying no unexpected equations'. One could ask for more; the construction above has produced a distributive, but not extensive, category whose Burnside rig is N[X]/(X^2(If it were extensive, it would be closed under taking summands, but every object in the larger category is a summand of G.) I don't know whether there is an extensive category with N[X]/(X^2Burnside rig; perhaps one or both of the examples John mentioned would do, if I knew what they were. While I'm airing my confusions, can anyone tell me what 'categorification' means? I don't know any such process; the simplest exanple, 'categorifying' natural numbers to get finite sets, seems to me rather 'remembering the finite sets and maps which gave rise to natural numbers by the abstraction of passing to isomorphism classes'. Finally, a note to John: While you're trying to give your audience some feeling for the virtues of n-categories, couldn't you give them a little help with ny being a little more precise about objects and maps? Greetings to all, and thanks for your patience while I got this stuff off my chest, Steve Schanuel