Group Theory: Free Abelian Groups

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Groups: Definitions, Properties, and Homomorphisms Log in to Mediaspace to watch this video

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Natural Transformations: Functors and Categories Log in to Mediaspace to watch this video

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Direct Sums: Abelian Groups Log in to Mediaspace to watch this video

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

Mayer-Vietoris Sequence Log in to Mediaspace to watch this video

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Free Abelian Groups and Homomorphisms Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Group Theory: Adjoint Functors and G-sets Log in to Mediaspace to watch this video

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Group Theory: Torsion and Divisibility Log in to Mediaspace to watch this video

Covers the concepts of torsion and divisibility in group theory.

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

The Lemma of the Five: Abelian Groups Log in to Mediaspace to watch this video

Presents the Lemma of the Five, a fundamental result in group theory.

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

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

Active Learning: Group Theory Log in to Mediaspace to watch this video

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group 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.

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