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Lecture
Natural Transformations: Definition
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Related lectures (32)
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Natural Transformations in Group Theory
Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
Natural Transformations: Examples
Introduces natural transformations through examples, covering equivalence of categories and functor properties.
Natural Transformations
Explores natural transformations between functors, emphasizing their composition-preserving properties and significance 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.
Equivalences of Categories
Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.
Introduction to Category Theory: Natural Transformations
Covers the concept of natural transformations between functors and their associativity.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Natural Learning Session
Explores coproducts, universal properties, and natural transformations in category theory.
Introduction to Category Theory: Equivalence of Categories
Covers the definition of equivalence of categories using natural transformations and provides concrete examples.
Functor Categories Composition and Induced Functors
Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.
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.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Active Learning Session
Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.
Natural Transformations: Adjunctions and Triangular Identities
Explores adjunctions, triangular identities, and natural transformations in category theory.
Introduction to Category Theory: Functors
Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.
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