On the K\"onigs function of semigroups of holomorphic self-maps of the unit disc

Let $(\phi_t)$ be a semigroup of holomorphic self-maps of~$\mathbb D$. In this note, we use an abstract approach to define the K\"onigs function of $(\phi_t)$ and "holomorphic models" and show how to deduce the existence and properties of the infinitesimal generator of $(\phi_t)$ from this construction.