A seminal result by Lovász states that two digraphs A and B (possibly with loops) are isomorphic if and only if for every digraph X the number of homomorphisms X → A equals the number of homomorphisms X → B. Lovász used this result to deduce certain cancellation properties for the direct product of digraphs. We develop an analogous result for the class of digraphs without loops, and with weak h...

For any class C und closed under NC reductions, it is shown that all sets complete for C under first-order (equivalently, Dlogtimeuniform AC) reductions are isomorphic under first-order computable

We provide a patch to complete the proof of the Voevodsky-Rost Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture).