[Y_Y]

My category theory is pretty rusty, but I'm not following the section on hom-sets. In particular:

  Hom(OrderService, InventoryService) = {
    checkAvailability: Order → Availability,
    reserveItems: Order → Reservation,
    releaseReservation: ReservationId → Unit,
    decrementStock: Order → Unit
  }

doesn't make sense to me as a hom-set between objects in our category of services, nor as a hom-functor considering one of {OrderService,InventoryService} to be a category and the other and object or morphism within the category.

In the first case all the morphisms in the hom-set should have the same type, and the second doesn't make sense semantically.

Hence it should be the hom-bifunctor considering both as categories, but then we should get natural tranformations in the answer.

I assume there's some notational abuse going on that I'm not picking up on. Either way it would be nice if someone more adept could clarify.