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Lecture
Group Actions and Functors
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Related lectures (32)
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Group Theory: Adjoint Functors and G-sets
Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Equivalences of Categories
Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.
Active Learning Session: Group Theory
Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.
Active Learning in Category Theory
Explores examples of categories, morphisms, groupoids, and functors in category theory.
Category Theory: G-sets and Left Adjoint Functor
Explores the construction of G-sets and left adjoint functors in category theory.
Group Theory: Subgroups and General Group Actions
Explores group actions, defining functors on groups, and verifying properties of group actions.
Category Theory: Introduction
Explores the concept of category theory, providing examples and discussing the opposite category concept.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Natural Transformations in Group Theory
Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.
Introduction to Category Theory: Adjoint Functors
Introduces adjoint functors in category theory, emphasizing their significance and applications in establishing relationships between different categories.
Equivalences de Catégories et Adjonctions
Explores category equivalences, adjunctions, and group actions in category theory.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
Introduction to Category Theory: Functors
Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Active Learning: Group Theory
Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
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