 Categories themselves admit a further generalization to 2-categories as algebras over two-dimensional graphs, with associative composition of 1-cells generalized to the 2-associative pasting of 2-cells. A further simplification of the free-algebra machinery then obtains, namely via abstract adjunctions as the natural 2-dimensional counterpart of isomorphisms in a category, which in turn is the natural 1-dimensional counterpart of equality of elements in a set, the 0-dimensional idea that two points can turn out to be one. This leads to a notion of abstract monad as simply the composition of an adjoint pair of 1-cells, one of which is the 1-cell abstracting the functor \(F\) that manufactures the free algebra \(F(V)\) from \(V\). Ordinary or concrete monads arise as the composition of functors as concrete 1-cells of a 2-category of categories.