Lectures related to Lie Algebra Homomorphisms

Covers special cases in group theory, focusing on group actions and functors.

Introduces the concept of restriction functors in group actions.

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

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

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

Introduces functors in category theory and explains their composition.

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

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.