  Type-and-effect systems incorporate information about the computational
effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase
may invoke alongside its return value. A semantics for type-and-effect systems
involves a parameterised family of monads whose size is exponential in the
number of effects. We derive such refined semantics from a single monad over a
category, a choice of algebraic operations for this monad, and a suitable
factorisation system over this category. We relate the derived semantics to the
original semantics using fibrations for logical relations. Our proof uses a
folklore technique for lifting monads with operations.
