A monad with arities'' is a monad T on some category K together with some extra data expressing the basicshapes'' of the operations involved in the structure of a T-algebra. There is a general result, called the nerve theorem, which in the case where K is a presheaf category, shows that the notion of monad with arities is an efficient reformulation of the notion of limit sketch''. The nerve theorem is so named because it generalises the characterisation of the simplicial sets that arise as nerves of categories. Other interesting instances of this result relevant for higher dimensional algebra involvelocal right adjoint monads'' -- such a T comes with a canonical choice of arities. These examples formalise the passage between the operadic and simplicial approaches to higher category theory.