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Lecture
Functors and Adjunctions
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Related lectures (32)
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Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Equivalences of Categories
Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.
Group Theory: Adjoint Functors and G-sets
Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.
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.
Natural Transformations: Categories, Functors, and Equivalence
Covers natural transformations between functors, identity transformations, and equivalence of categories.
Category Theory: G-sets and Left Adjoint Functor
Explores the construction of G-sets and left adjoint functors in category theory.
Active Learning Session
Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.
Theory: Adjunctions
Introduces adjunctions between categories, emphasizing equivalence and natural transformations.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
