Lecture

Relation between Direct Sum and Hom

Description

This lecture explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B, based on the proposition that for a given set X and {Ax | x ∈ X} in Ab, there exists a clear relationship. The proof involves showing the isomorphism between Hom(A, B) and Hom(A, B) through a specific mapping. The lecture also delves into the underlying sets of abelian groups and the importance of demonstrating specific relationships within them, leading to a deeper understanding of the connection between direct sums and Hom functors.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (48)
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Algebraic Kunneth Theorem
Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.
Hom Functor: Abelian Groups
Explores the Hom functor for abelian groups and its relation to direct sums.
Cross Product in Cohomology
Explores the cross product in cohomology, covering its properties and applications in homotopy.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
Show more