Defining A-infinity Structures in Monoidal DG Categories

Explore a comprehensive lecture on A-infinity structures in monoidal DG categories presented by Rina Anno at the M-Seminar, Kansas State University. Delve into the traditional definition of an A-infinity algebra as a graded vector space with specific operations and relations. Examine the concept of an A-infinity algebra object within an arbitrary monoidal DG category, and discover how results and constructions translate into this setting. Learn about the main application: constructing the category of A-infinity modules over a DG lift of a monad produced by adjoint functors between enhanced triangulated categories. Investigate the analog of the Barr-Beck theorem for enhanced triangulated categories. Gain insights from this joint work with T. Logvinenko and S. Arkhipov, presented in a 1 hour and 29 minute talk that offers a deep dive into advanced mathematical concepts.