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Category Equivalence
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Related lectures (32)
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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.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Relation between Direct Sum and Hom
Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Active Learning Session
Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.
Homotopical Algebra: (Co)Limits
Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.
