The author's previous post goes into details of a categorial connection:

  λ-Calculus, Combinatory Logic and Cartesian Closed Categories
  https://thma.github.io/posts/2021-04-04-Lambda-Calculus-Combinatory-Logic-and-Cartesian-Closed-Categories.html

Also, more in-depth:

  Categorical combinators, P.-L. Curien
  https://www.sciencedirect.com/science/article/pii/S001999588680047X

(or maybe you're looking for something beyond that)