Lectures related to Group Theory: Special Cases

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Covers the adjoints of the restriction functor in group theory.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

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

Explores the Hom functor for abelian groups and its relation to direct sums.

Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Introduces functors in category theory and explains their composition.

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Introduces subgroups and homomorphisms in group theory, with examples for illustration.