Definition. Object-discrete T-monoid [mde-J9P7]

A \(T\)-monoid \(M : A \nrightarrow TA\) for \(T\) a monad on \(\textsf {Mod}(\mathbb {X})\), where \(\textsf {Mod}\) is the monads and bimodules construction, is object-discrete if \(A : A_0 \nrightarrow A_0\), which by definition is a monad in \(\mathbb {X}\), is isomorphic to (the unique monad on) \(\textsf {id}_{A_0} : A_0 \nrightarrow A_0\).