Co- and Contra-categories: Theory of Decomposition and Directed Obstructions

Learn about cocategory theory and contra-categories in this advanced mathematics seminar talk from the Topos Institute Berkeley series. Explore how decomposition, rather than composition, serves as the central operation in this theoretical framework developed by Alexander Gietelink Oldenziel and Jade Master. Delve into the formalization of directed obstructions and their connections to apartness spaces, Lawvere metric spaces, and ultrafilters. Follow along as the presentation covers key concepts including introductory definitions, structural elements, various examples, preorder categories, ultrafilters, and categorical construction. Examine the relationship between traditional category theory and this novel approach to mathematical composition through detailed explanations of coassociativity, contragraph examples, and free construction methods.