Categories and Functors

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Related lectures (32)

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

Category Theory: Introduction

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

Functors: Definition

Introduces functors in category theory and explains their composition.

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Categories: Functors, and Natural Transformations

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Limits and Colimits: Equalizers and Coequalizers

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Active Learning Session

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

Limits and colimits: Concrete Examples

Explores concrete examples of limits and colimits in functors and different categories.

Natural Learning Session

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

Active Learning Session: Group Theory

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

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.

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