Word problems on string diagrams - Delpeuch, A (2021)
String diagrams are graphical representations of morphisms in various sorts of categories. The mathematical results which establish their soundness and completeness provide an elegant bridge between algebra and topology, equating a certain class of topological deformations to the equational theory of an algebraic structure. Beyond this conceptual appeal they also are practical tools to reason in the corresponding categories, making it easy to build intuition about the combinatorics of morphisms and efficiently communicate proofs to peers. Finally, they provide data structures to encode morphisms and manipulate them with computer programs such as proof assistants. Our contributions to the field explore three main directions.