Category Theory: Introduction

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Related lectures (32)

Page 3 of 4

Introduction to Category Theory

Covers the introduction to categories, including definitions and examples.

Limits and colimits: Introduction, Chapter 1(c)

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

Introduction to Category Theory: Functors

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

Active Learning Session: Group Theory

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

Introduction to Category Theory: Natural Transformations

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

Natural Transformations Composition

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

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.

Group Morphisms: G-equivariant, Chapter III

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

Model Categories and Homotopy Theory: Functorial Connections

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Functors: Categories, Functors, and Natural Transformations

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