Can any category be imbedded in a balanced category? It is a simple fact that any retract is an epimorphism, and that in a sub-category a retract preserves its epic property (the same for co-retract and monomorphism). My question is: is the only reason that a epimorphism fails to be a retract is the "cutting out" of its left inverse from some "bigger" category? Or are there other problems? If this is the only problem, it means that we could "enlarge" the category, making each monic+epic a retract+co-retract and a isomorphism in the "bigger" category ,and then also an isomorphism in the original. Or in other words, there is an imbedding into a balanced category.

Every presheaf category is balanced, so the Yoneda embedding does the job.