The author discusses a calculational approach to category theory introduced by Fokkinga and Meertens, highlighting the benefits and drawbacks compared to traditional proofs by diagram pasting. They propose the use of string diagrams to combine the strengths of both approaches, retaining type information while pursuing a more calculational form of proof. String diagrams offer a topological perspective on categorical proofs, handling functoriality and naturality conditions effortlessly. The author systematically applies graphical techniques to various aspects of category theory, developing diagrammatic formulations for common notions like adjunctions, monads, and Kan extensions. They use these graphical tools to prove standard results in a proposed diagrammatic style.
https://arxiv.org/abs/1401.7220