Adithya Murali worked on the small category of *deterministic matrices*: the vertices are the pairs *(p,q)* of natural integers, the arrows from *p* to *q* are matrices of languages such that each row is a *q*-tuple of pairwise disjoint languages, whose union is a prefix-language.

Though this algebraic structure has already been used in several works in formal language theory, a systematic study is still lacking. Along these lines, Adithya Murali has:

– expanded a sketchy manuscript of the supervisor into a firm formal framework,

– increased the knowledge on equations in this structure, namely by making sound an interesting finiteness result on equations (the *shears* lemma) and contributing to its proof.

This work, though not finished, will constitute a research-report.