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Explore the intersection of formal mathematics and category theory in this seminar presentation that introduces the Lean theorem prover and its application to monoidal category theory. Learn about Lean's capabilities for mathematical formalization with computer-verified correctness, and discover how monoidal category theory has been implemented in Mathlib, Lean's comprehensive mathematics library. Examine the technical aspects of Lean's metaprogramming framework and understand how it handles the coherence theorem in monoidal categories, showcasing the powerful synergy between functional programming and formalized mathematics. Gain insights into the practical applications of theorem proving in advanced mathematical structures, with specific focus on 2-category theory formalization. The presentation includes detailed explanations of the theoretical foundations, practical implementation strategies, and demonstrates how modern proof assistants are revolutionizing mathematical research and verification processes.
