Lectures related to Active Learning Session: Group Theory

Adjunctions and Limits: Exploring Functors and Co-limits

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

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Equivalences of Categories

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

Linear Applications and Simple Objects

Covers the bijection between linear applications from L(X) to V and applications from X to U(V).

Category Theory: Introduction

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

Equivalences de Catégories et Adjonctions

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

Active Learning in Category Theory

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

Group Theory Fundamentals

Introduces the basics of group theory, defining groups, categories, and groupoids.

Group Actions and Functors

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

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Active Learning Session

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

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.

Homotopical Algebra

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

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Adjunctions: Constructing Desired Adjoints

Explores constructing desired adjoints in specific categories like Set.

Examples, Chapter 1(b): Adjunctions

Presents concrete examples of adjunctions between Set and Top categories.

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.