Monads and theories (Q2001598)

Given a locally presentable enriched category \(\mathcal{E}\) together with a small dense full subcategory \(\mathcal{A}\) of arities, the authors study the relationship between monads on \(\mathcal{E}\) and identity-on-objects functors out of \(\mathcal{A}\). This leads to an equivalence between \(\mathcal A\)-nervous monads and \(\mathcal{A}\)-theories extending allmost all previously known monad-theory correspondences.