Lectures related to Initial and terminal objects

Explores concrete examples of limits and colimits in functors and different categories.

Explores the concept of (co)limits in homotopical algebra, discussing functor relations, special cases, and the universal properties of colimits and limits.

Functor Fixed Points and Orbital Functor

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

Introduction to Categories: Products and Coproducts

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Natural Transformations: Functors and Categories

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

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

Functors: Definition

Introduces functors in category theory and explains their composition.

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Category Theory: G-sets and Left Adjoint Functor

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

Group Theory: Restriction Functor

Explores the restriction functor in group theory, focusing on its properties.

Restriction Functors: Group Actions

Introduces the concept of restriction functors in group actions.

Group Morphisms: G-equivariant, Chapter III

Discusses the formulation of G-morphisms within vector spaces and topological spaces.