Lectures related to Functor Categories Composition and Induced Functors

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

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

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

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.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Categories and Functors

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

Simplicial and Cosimplicial Objects: Examples and Applications

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

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.

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.

Introduction to Category Theory: Natural Transformations

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

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.

Functors: Categories, Functors, and Natural Transformations

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

Active Learning in Category Theory

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