Lectures related to Active Learning: Group Theory

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Group Theory: Adjoint Functors and G-sets

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

Equivalences of Categories

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

Group Actions and Functors

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

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Group Actions: Equivariance and Functors

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

Group Theory: Torsion and Divisibility

Covers the concepts of torsion and divisibility in group theory.

Category Theory: Introduction

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

Active Learning Session

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

Group Theory: Subgroups and General Group Actions

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

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Category Theory: G-sets and Left Adjoint Functor

Explores the construction of G-sets and left adjoint functors in category theory.

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Active Learning in Category Theory

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

Torsion: Hom Functoriality and Exact Sequences

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Group Theory: Free Abelian Groups

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

Equivalences de Catégories et Adjonctions

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

Group Theory: Special Cases

Covers special cases in group theory, focusing on group actions and functors.