# Research

Here are some current and past research papers and preprints that I have written. Feel free please email me at rachman.jm@gmail.com with any suggestions or corrections that you would like to propose.

### Preprints

 Category-Theoretic Generalization of Higman’s Lemma Admits Applicability and Constructive Proof. Last Update: (April 2016). Higman’s Lemma, a special case of Kruskal’s Tree Theorem, provides fascinating results in the areas of combinatorics, logic, and theoretical computer science. Recent papers that have presented new formulations and constructive proofs of Higman’s Lemma are all quite similar in terms of computation. These computational formulations lack applications in other fields of mathematics. In this paper, we give a new proof of Higman’s Lemma as well as a number of new applications. These results are obtained by suitably categorifying the lemma using free monoidal monads, Kleisli categories, and Elienberg-Moore categories. Our proof allows us to avoid unnecessary reference to computability. By this categorification, we are able to present a new constructive, category-theoretic proof of Higman’s Lemma. The generalization of this lemma leads us into applications in $\infty$-categories and (higher) algebraic geometry which shall be further discussed. PDF