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Homotopical Algebra: Examples and Adjunctions
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Related lectures (32)
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Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Limits and colimits: Concrete Examples
Explores concrete examples of limits and colimits in functors and different categories.
Homotopical Algebra
Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.
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Provides an overview of categories, functors, and natural transformations in mathematics.
Functors: Categories, Functors, and Natural Transformations
Introduces functors, including identity and forgetful functors, and explores duality functors.
Introduction to Derived Functors: Left and Right Derived Functors
Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Limits and Colimits: Understanding Categories
Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.
Active Learning Session: Group Theory
Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
