Category Theory Using String Diagrams (2014)

The paper "Category Theory Using String Diagrams" by Daniel Marsden introduces a novel approach to category theory by utilizing string diagrams. These diagrams aim to combine the advantages of calculational reasoning with the retention of vital type information present in traditional proofs by diagram pasting. By employing graphical representations, the paper explores various concepts in category theory such as adjunctions, monads, Kan extensions, limits, and colimits. The use of string diagrams provides a topological perspective on categorical proofs, simplifying the handling of functoriality and naturality conditions that can be cumbersome in conventional notation. Through examples and graphical techniques, the paper demonstrates how these diagrams can be used to prove standard results in a more intuitive and visually appealing manner. This innovative approach offers a fresh perspective on category theory, bridging the gap between calculational methods and diagrammatic reasoning.