Category Theory Reading Group

This reading group will work through Conceptual Mathematics: A first introduction to categories by F. William Lawvere and Stephen H. Schanuel. About the Book Category theory is a branch of mathematics that focuses on the relationships between objects (maps) rather than the internal structure of the objects themselves. This specific text is designed as an entry point for those without a background in advanced mathematics. It uses elementary concepts, such as finite sets, directed graphs, and discrete dynamical systems, to illustrate fundamental categorical principles. Structure The book is organized into "Articles," which present core theoretical concepts, and "Sessions," which are based on actual classroom discussions and contain exercises to help clarify the theory. Core Topics The group will cover the following five parts of the text: - Part I: The Category of Sets. Introduction to sets, maps, and the composition of maps. - Part II: The Algebra of Composition. Exploring isomorphisms, sections, retractions, and the "division" of maps. - Part III: Categories of Structured Sets. Applying categorical thinking to endomaps, directed graphs, and sequences of states. - Part IV: Elementary Universal Mapping Properties. Defining terminal/initial objects, products, and sums within a categorical framework. - Part V: Higher Universal Mapping Properties. An introduction to map objects (exponentiation), function spaces, and the basic logic of toposes. Goal The objective of this group is to gain familiarity with the "categorical method." This involves learning how to unify different mathematical ideas—from arithmetic to logic—through the study of composition and universal properties. Participants will be expected to read the assigned sections and work through the exercises found in the Sessions chapters.