The algebra of embeddings at the I3 level has been deeply analyzed, but nothing is known algebra-wise for embeddings above I3. In this article, we introduce an operation for embeddings at the level of I0 and above, and prove that they generate an LD-algebra that can be quite different from the one implied by I3.
"LD-Algebras Beyond I0." Notre Dame J. Formal Logic 60 (3) 395 - 405, August 2019. https://doi.org/10.1215/00294527-2019-0009