As far as I know, there is no "official" notation for the left adjoint of a functor $F : \mathcal{C} \to \mathcal{D}$ if it exists. I have seen the notation $F^*$ sometimes, but this looks only nice when $F$ is already written as $F_*$, which is not practical. (This notation is then motivated by direct and inverse image functors. And it seems to be quite common for adjunctions between preorders aka Galois connections.) Similarly, I have seen the notation $F_*$ for the right adjoint of $F$, which only looks nice when $F$ is already written as $F^*$. I have also seen the notation $F^{\dagger}$ for the right adjoint, which looks nice, but then how would you denote the left adjoint if it exists? Perhaps ${}^{\dagger} F$? I don't want to start a debate here what is a good notation or not, since this is subjective anyway and is not suited for mathoverflow. I would like to know:

**Are there any textbooks, influential papers or monographs on category theory which have introduced a notation for the left adjoint of $F$? Is there any notation which has been used by multiple authors?**

Just to avoid any misunderstanding: Of course there is the official notation $F \dashv G$ when $F$ is left adjoint to $G$, but $\dashv$ is a relation symbol. I am interested in a function symbol (which makes sense since left and right adjoints are unique up to canonical isomorphism if they exist).