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Related lectures (34)

Category Theory: G-sets and Left Adjoint Functor Log in to Mediaspace to watch this video

Explores the construction of G-sets and left adjoint functors in category theory.

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

Introduces natural transformations in category theory through concrete examples from group theory.

Free Abelian Groups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of free abelian groups as an important left adjoint functor.

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Introduction to Category Theory: Functors Log in to Mediaspace to watch this video

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Introduction to Category Theory: Adjoint Functors Log in to Mediaspace to watch this video

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

Natural Learning Session Log in to Mediaspace to watch this video

Explores coproducts, universal properties, and natural transformations in category theory.

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

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

Introduction to Category Theory: Equivalence of Categories Log in to Mediaspace to watch this video

Covers the definition of equivalence of categories using natural transformations and provides concrete examples.

Equivalences de Catégories et Adjonctions Log in to Mediaspace to watch this video

Explores category equivalences, adjunctions, and group actions in category theory.

Limits and Colimits: Understanding Categories Log in to Mediaspace to watch this video

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.

Group Theory: Subgroups and General Group Actions Log in to Mediaspace to watch this video

Explores group actions, defining functors on groups, and verifying properties of group actions.

Characteristic Polynomials and Similar Matrices Log in to Mediaspace to watch this video

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Matrix Operations: Products and Properties Log in to Mediaspace to watch this video

Covers the definition of associated matrices, matrix products, image vectors, and isomorphisms.

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