Functors and Homomorphisms in Group Theory

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 3 of 4

Group Actions and Functors

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

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Group Actions: Equivariance and Functors

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

Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

Relation between Direct Sum and Hom

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Endomorphisms and automorphisms of totally disconnected locally compact groups V

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing surjective homomorphisms and free abelian groups.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Introduction to Category Theory: Natural Transformations

Introduces natural transformations in category theory through concrete examples from group theory.

Free Product: Group Theory

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.