Monoid homomorphisms and comprehensions

The formalism presented here is based on [9] and assumes familiarity with the notions and notations summarized in Appendix Section A.2. I will use the programming view of monoids exposed there using the specific notation of monoid attributes, in particular for sets, bags, and lists. I will also assume basic familiarity with naive $\lambda$-calculus and associated typing as presented in Appendix Section A.3.