Concept

Category (mathematics)

Related lectures (32)

Category Theory: Introduction

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

Categories and Functors

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Active Learning in Category Theory

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

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Active Learning Session: Group Theory

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

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.

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.

Natural Learning Session

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

Examples, Chapter 1(b): Adjunctions

Presents concrete examples of adjunctions between Set and Top categories.

Functors: Examples

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.

Category Theory: Introduction

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Group Quotients and Push-outs

Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.

Adjunctions and Functor Categories: Exploring Connections

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

Introduction to Categories: Products and Coproducts

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.