Lectures related to Equivalence of categories

Adjunctions and Limits: Exploring Functors and Co-limits

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

Introduction to Category Theory: Natural Transformations

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

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

Category Theory: Introduction

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

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Categories: Functors, and Natural Transformations

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Linear Applications and Simple Objects

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

Group Theory: Recalls

Offers a recap on group theory, focusing on linear applications and bases.

Natural Transformations: Functors and Categories

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

Homotopical Algebra

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

Properties of Cartesian Products and Disjoint Unions

Introduces essential properties of Cartesian products and disjoint unions in the theory of groups and categories.

Natural Transformations: Epsilon Transformation

Explores the epsilon transformation in group theory and category theory, emphasizing linearity and naturality.

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Active Learning Session: Group Theory

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

Introduction to Group Theory: Motivation

Introduces adjunctions in Group Theory with examples of natural transformations and isomorphisms.

Categories and Functors

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

Vector Space Dimension and Bases

Covers the concept of dimension in a vector space and bases.

Category Theory: Natural Transformations and Adjunctions

Explores natural transformations and adjunctions in category theory, illustrating concepts through concrete examples and discussing the conditions for the existence of adjoints.

Introduction to Category Theory: Adjunctions (Part 1)

Explores the definition of adjunctions and the relationship between functors.

Functors: Categories, Functors, and Natural Transformations

Introduces functors, including identity and forgetful functors, and explores duality functors.