Group Theory: Special Cases

Related lectures (31)

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Explores two definitions of group action on a set, focusing on properties and applications.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Delves into the categorical framework for group actions and the correspondence between G-actions on c and functors from BG to C.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

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

Covers the concepts of torsion and divisibility in group theory.

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

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

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

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.