We show that the epimorphism problem is solvable for targets are virtually cyclic or a product of an Abelian group and finite group.

In this paper we study the problem of deciding the existence of a subgraph epimorphism between two graphs. Our interest in this variant of graph matching problem stems from the study of model reductions in systems biology, where large systems of biochemical reactions can be naturally represented by bipartite digraphs of species and reactions. In this setting, model reduction can be formalized a...

We show that every Π1-elementary epimorphism between models of ZF is an isomorphism. On the other hand, nonisomorphic Σ1-elementary epimorphisms between models of ZF can be constructed, as can fully elementary epimorphisms between models of ZFC−. Elementary epimorphisms were introduced by Philipp Rothmaler in [Rot05]. A surjective homomorphism f : M → N between two model-theoretic structures is...

We show that there exist infinitely many examples of pairs of knots, K1 and K2, that have no epimorphism π1(S 3 \K1)→ π1(S \K2) preserving peripheral structure although their A-polynomials have the factorization AK2(L,M) | AK1(L,M). Our construction accounts for most of the known factorizations of this form for knots with 10 or fewer crossings. In particular, we conclude that while an epimorphi...