Lectures related to Universal Property Verification in GC

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.

Natural Transformations: Examples and Applications

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

Categories and Functors: An Introduction

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

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.

Natural Learning Session

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

Limits and colimits: Introduction, Chapter 1(c)

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

Natural Transformations

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

Category Theory: G-sets and Left Adjoint Functor

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

Introduction to Category Theory: Natural Transformations

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

Functor Categories Composition and Induced Functors

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

Active Learning Session

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

Free Abelian Groups: Group Theory

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

Restriction Functors: Group Actions

Introduces the concept of restriction functors in group actions.

Natural Transformations in Group Theory

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Natural Transformations: Definition

Covers the definition and properties of natural transformations between functors in category theory.

Limits and colimits as adjoints: Chapter 1(c)

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

Functors: Definition

Introduces functors in category theory and explains their composition.

Active Learning in Category Theory

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