Explore the fifth lecture in a series on diagrammatic categories in algebra presented by Emily Peters. Delve into a specific example of diagrammatic categories and its unique formalism within the context of quantum symmetries, tensor categories, topological quantum field theories, and vertex algebras. Gain insights into how these diagrammatic representations are utilized across various subfields of algebra. Analyze the presented example and consider potential generalizations to other areas of mathematics. This 51-minute talk, part of a workshop organized by the Centre de recherches mathématiques (CRM), offers an in-depth look at the intersection of category theory and diagrammatic representations in advanced algebraic structures.