I would like to learn some fundamental facts (that don't seem to be visible in Makkai and Pare', although I may be overlooking them) about jus how sketchable is a generalization of equational: 1. It seems clear that the models of an equational theory (a category algebraic over Sets) is sketchable. I'm thinking of a product sketch on (the opposite of) the Kleisli category. But is such a category accessible, or only in the case the theory has rank (a cardinal bound on the arities of the operations) ? 2. Are model categories for equational theories on an arbitrary base category again sketchable over Sets via the same construction suggested above? 3. Is there such a thing as a canonical sketch, a kind of complete syntactic description of a sketchable theory? And if so, is there an adunction between syntax and semantics?