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This colloquium talk from the Topos Institute explores how universal coalgebra theory can extend traditional algebraic social network analysis beyond pairwise relationships to include higher-order interactions. Learn how to formalize social roles and positions in graph-based social systems and discover their generalization to hypergraph models that capture complex multi-actor interactions. The presentation connects these analytical approaches through functoriality results, offering a mathematical framework for understanding complex social structures. Based on collaborative research with Nima Motamed and Emily Roff, this 57-minute talk provides mathematical insights into modeling and analyzing sophisticated social systems.
