This seems to be the original source:

M. Barr and J. Beck, Acyclic models and triples, Proc. Conference Categorical Algebra (La Jolla, Calif., 1965) Springer, New York, 1966, pp. 336-343.

The "triple" is an older name for a monad (according to [Wikipedia](https://en.wikipedia.org/wiki/Beck%27s_monadicity_theorem) ).