Dual Algebraic Structures and Enrichment: From Sweedler Theory to Operadic Structures

Learn about the fundamental concepts of Sweedler theory for algebras and modules in this advanced mathematics colloquium talk from the Topos Institute. Explore the enrichment of algebra categories in coalgebra categories and the relationship between modules and comodules through an enriched fibration framework. Delve into the theoretical foundations, starting with basic motivations and progressing through complex topics including Hopf categories, universal measuring comodules, and double categories. Discover how these mathematical structures extend to operadic frameworks and their broader applications. The presentation systematically builds from core principles to advanced generalizations, making connections between different algebraic structures and their dual counterparts.