Lectures in course MATH-211: Algebra II - groups

Group Actions: Examples and Applications

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Introduction to Category Theory

Covers the introduction to categories, including definitions and examples.

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Introduction to Category Theory: Categories and Examples

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Functors and Natural Transformations

Delves into functors, natural transformations, and group actions with explicit examples.

Introduction to Category Theory: Functors

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

Equivalences de Catégories et Adjonctions

Explores category equivalences, adjunctions, and group actions in category theory.

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Group Theory: Adjoint Functors and G-sets

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Introduction to Category Theory: Natural Transformations

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

Adjunctions, Products, and Coproducts

Discusses adjunctions, products, and coproducts in category theory.

Introduction to Category Theory: Equivalence of Categories

Covers the definition of equivalence of categories using natural transformations and provides concrete examples.

Quotient Groups: Homomorphisms and Isomorphisms

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

Introduction to Category Theory: Adjunctions (Part 1)

Explores the definition of adjunctions and the relationship between functors.

Group Theory: Subgroups and General Group Actions

Explores group actions, defining functors on groups, and verifying properties of group actions.

Introduction to Category Theory: Adjoint Functors

Introduces adjoint functors in category theory, emphasizing their significance and applications in establishing relationships between different categories.

General Group Actions

Explores group actions on spaces, including fixed points and non-trivial actions.

Introduction to Category Theory: Adjoint Functors

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

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Introduction to Category Theory: Adjoint Functors

Introduces the concept of adjoint functors in category theory, focusing on the characterization of adjunctions.