Lectures related to Functors: Examples

Categories and Functors: An Introduction

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

Adjunctions and Functor Categories: Exploring Connections

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Natural Transformations: Examples and Applications

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

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance 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: 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.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Active Learning Session

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

Introduction to Category Theory: Natural Transformations

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

Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Functor Categories Composition and Induced Functors

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.

Active Learning in Category Theory

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

Natural Learning Session

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

Category Theory: Introduction

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

Limits and colimits as adjoints: Chapter 1(c)

Explores the characterization of limits and colimits as adjoints in category theory.

Introduction to Category Theory: Functors

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

Introduction to Category Theory: Natural Transformations

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