Functors and Homomorphisms in Group Theory

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (49)

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Group Actions: Equivariance and Functors Log in to Mediaspace to watch this video

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

Group Direct Sums in Group Theory Log in to Mediaspace to watch this video

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

Natural Transformations Log in to Mediaspace to watch this video

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

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

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

Active Learning Session Log in to Mediaspace to watch this video

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Group Theory Basics Log in to Mediaspace to watch this video

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Group Theory: Torsion and Divisibility Log in to Mediaspace to watch this video

Covers the concepts of torsion and divisibility in group theory.

Two Definitions of Group Action Log in to Mediaspace to watch this video

Explores two definitions of group action on a set, focusing on properties and applications.

Group Actions and Functors Log in to Mediaspace to watch this video

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

Quotient Groups: Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Category Theory: Introduction Log in to Mediaspace to watch this video

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Introduction to Category Theory: Functors Log in to Mediaspace to watch this video

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Untitled Log in to Mediaspace to watch this video

Introduction to Category Theory: Adjoint Functors Log in to Mediaspace to watch this video

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

Group Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Endomorphisms: Matrix Equivalence Log in to Mediaspace to watch this video

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Applications of Lagrange's Theorem Log in to Mediaspace to watch this video

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Page 2 of 3