Title: String diagrams: by categories, for categories
Abstract: The formalization of string diagrams, in a 1991 paper by Andre Joyal and Ross Street, was a seminal event. They defined a basic diagrammatic language and proved its validity for rigorous mathematics in any monoidal category, and in doing so they laid the foundation for a substantial ongoing program of research on extensions and specializations of the original theory. This first half of this talk will address the question of how all this was possible – how it can be demonstrated that proofs by diagram are logically valid. We will introduce the foundations of string diagrams by studying the core argument of Joyal and Street’s 1991 paper. The second half will be devoted to a particular example: a lovely diagrammatic language for the 2-category of categories, as introduced in a recent monograph by Ralf Hinze and Dan Marsden. We will demonstrate how to use the language, and we will emphasize the benefits that it offers in the study of elementary category theory.