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Related lectures (32)

Natural Transformations: Definition

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

Limits and colimits: Introduction, Chapter 1(c)

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

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Natural Transformations in Group Theory

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

Products: Theory of Categories

Covers the concept of products in category theory, focusing on their properties, uniqueness, and isomorphisms.

Natural Transformations: Examples

Introduces natural transformations through examples, covering equivalence of categories and functor properties.

Introduction to Coproducts

Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.

Triangular Identities

Covers triangular identities, natural transformations, commutative diagrams, and adjunction notation in group and category theory.

Natural Transformations: Adjunctions and Triangular Identities

Explores adjunctions, triangular identities, and natural transformations in category theory.

Limits and colimits as adjoints: Chapter 1(c)

Explores the characterization of limits and colimits as adjoints 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.

Simplicial and Cosimplicial Objects: Examples and Applications

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

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 in Model Categories: An Overview

Provides an overview of lifting properties in model categories, focusing on their definitions and implications for morphisms and commutative diagrams.

Introduction to Adjunctions in Category Theory

Introduces adjunctions in category theory, exploring necessary conditions and natural transformations for adjoint functors.

Limits and Colimits in Functor Categories

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

Group Quotients and Push-outs Log in to Mediaspace to watch this video

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

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Introduction to Category Theory: Adjoint Functors Log in to Mediaspace to watch this video

Introduces the concept of adjoint functors in category theory, focusing on the characterization of adjunctions.

Natural Transformations in Algebra Log in to Mediaspace to watch this video

Explores natural transformations in algebra, defining functors and isomorphisms.

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