Limits and Colimits: Understanding Categories

This lecture delves into the concepts of limits and colimits in category theory, exploring their definitions, properties, and applications. The instructor discusses the non-existence of limits in certain categories and the completion of categories by adding missing limits. Theoretical considerations on the duality of limits and colimits are also covered, along with the relationships between limits and colimits under functors. Special cases, such as the empty category and specific functors, are analyzed to provide a comprehensive understanding of these fundamental concepts.