  The investigation and classification of non-unique factorization phenomena
have attracted some interest in recent literature. For finitely generated
monoids, S.T. Chapman and P. Garcia-Sanchez, together with several co-authors,
derived a method to calculate the catenary and tame degree from the monoid of
relations, and they applied this method successfully in the case of numerical
monoids. In this paper, we investigate the algebraic structure of this
approach. Thereby, we dispense with the restriction to finitely generated
monoids and give applications to other invariants of non-unique factorizations,
such as the elasticity and the set of distances.
