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Explore a mathematical seminar from Oxford that delves into the preservation of 2-algebraic structure by pseudo-functors, examining how universal algebra's concepts extend to categorical structures. Learn about the fundamental differences between traditional universal algebra dealing with sets and 2-algebra focusing on categories with operational structures and natural transformations. Discover how functorial semantics, developed by Lawvere for algebra and extended by Power, Lack, and others for 2-algebra, enables interpretation of algebraic theories beyond their original contexts. Examine practical examples like symmetric monoidal categories and categories with finite products, and understand how these concepts extend to 2-categories beyond Cat. Investigate the crucial question of how cartesian pseudo-functors preserve 2-algebraic structure, particularly focusing on flexible 2-algebraic theories where equations exist between transformations rather than operations.
