$\quad$1. An adjunction $\xymatrix{\cC \ar@<1ex>[r]^F \ar@{}[r]\mid\perp & \mathsf{D} \ar@<1ex>[l]^U}$ is monadic if the canonical comparison functor of Proposition \ref{prop:monad-universal} from $\mathsf{D}$ to the category of algebras for the induced monad on $\mathsf{C}$ defines an equivalence of categories.\n2. A functor $U \colon \mathsf{D} \to \mathsf{C}$ is monadic if it admits a left adjoint that defines a monadic adjunction.