Internalization, String Diagrams, and Hochschild Cohomology

Carter, Crans, Elhamdadi, and Saito have introduced an analogue of the group algebra for self-distributive algebras called “shelves”, which relate to the structures of both Lie algebras and quandles.
They use a diagrammatic method to present a cohomology theory
encompassing both Lie algebra and quandle cohomology.
Here we will consider this method of string diagrams and its relation to Lawvere’s theory categories and internalization of algebraic structures.