Lectures related to Relation between Direct Sum and Hom

Untitled

Direct Sums of Abelian Groups

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Mayer-Vietoris Sequence

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Abelian Groups: Free Abelian Groups

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

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Divisibility and Torsion

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