Let $F: A \to B$ and $G: B \to A$ be adjoint functors, with $F \dashv G$. There is a full subcategory $A'$ of $A$ consisting of those objects $a$ for which the unit map $a \to GF(a)$ is an isomorphism, and there is a dually-defined full subcategory $B'$ of $B$. It is an elementary exercise to show that $F$ and $G$ restrict to an equivalence $A' \simeq B'$.

Either of the equivalent categories $A'$ and $B'$ is called the invariant part or fixed category of the adjunction. There are other names too; the terminology hasn't settled down.

Q. Where did this general construction first appear in print?

Adjoint functors were introduced by Kan in 1958. I don't see this construction in his paper. But I guess someone must have mentioned or used it quite soon thereafter. I want to know who I should cite.

Let me make clear that I'm not asking about particular instances of this construction. It's the general construction I'm after. I'm also interested in early references in which the general construction plays a significant part, even if they're not the original source.