Group Actions and Functors

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Related lectures (32)

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Group Theory Fundamentals

Introduces the basics of group theory, defining groups, categories, and groupoids.

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.

Limits and colimits: Introduction, Chapter 1(c)

Introduces limits and colimits in a category, covering their properties and uniqueness.

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Generalization of Category Equivalence

Introduces an important generalization of category equivalence and its implications for group theory.

Natural Transformations: Definition

Covers the definition and properties of natural transformations between functors in category theory.

Introduction to Category Theory: Adjoint Functors

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

Natural Learning Session

Explores coproducts, universal properties, and natural transformations 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.

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