I have two reference questions
What should be required of a category with finite products so that a (multi-sorted, finitary) Lawvere theory to induce monadic adjunction in it? This should be perfectly standard (I think I saw it a month ago), but now I can't find it in books, nlab or MO.
What should be required from the model category so that the category of algebras of a (multi-sorted, finitary) Lawvere theory in it has the right transferred model structure?