Lectures related to Functors: Definition

Natural Transformations: Examples and Applications

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

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

Natural Learning Session

Explores coproducts, universal properties, and natural transformations in category theory.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Group Theory: Restriction Functor

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

Active Learning in Category Theory

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

Category Theory: Introduction

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

Restriction Functors: Group Actions

Introduces the concept of restriction functors in group actions.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Categories and Functors

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

Group Morphisms: G-equivariant, Chapter III

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

Introduction to Category Theory: Natural Transformations

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

Natural Transformations: Functors and Categories

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

Left Adjoint Preserves Coproducts

Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.

Limits and colimits: Introduction, Chapter 1(c)

Introduces limits and colimits in a category, covering their properties and uniqueness.

Limits and Colimits: Understanding Categories

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.

Introduction to Category Theory: Functors

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