Humans use analogies to link seemingly unrelated domains. A mathematician might discover an analogy that allows them to use mathematical tools developed in one domain to prove a theorem in another. Someone could recommend a book to a friend, based on understanding their hobbies, and drawing an analogy between them. Recommender systems typically rely on learning statistical correlations to uncover these cross-domain correspondences, but it is difficult to generate human-readable explanations for the correspondences discovered. We formalise the notion of 'correspondence' between domains, illustrating this through the example of a simple mathematics problem. We explain how we might discover such correspondences, and how a correspondence-based recommender system could provide more explainable recommendations.