In computer science, the Kleisli maps of a monad are interpreted as effectful computations which may interact with an environment or resource. We might ask whether we can recover a description of this environment abstractly from the monad. We call this the monad’s spectrum, just as the spectrum of a ring is a description of its domain space, when we think of the ring as a ring of functions. In this talk I will discuss my ongoing joint work with Richard in understanding the spectrum. In particular, we show that it is an instance of Diers’ general notion of spectrum for a right multi-adjoint.