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Category theory
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Related lectures (32)
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Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
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.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Products: Theory of Categories
Covers the concept of products in category theory, focusing on their properties, uniqueness, and isomorphisms.
Natural Transformations: Definition
Covers the definition and properties of natural transformations between functors in category theory.
Natural Transformations in Group Theory
Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.
Functors: Definition
Introduces functors in category theory and explains their composition.
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Functors: Examples
Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.
Introduction to Coproducts
Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.
Limits and colimits as adjoints: Chapter 1(c)
Explores the characterization of limits and colimits as adjoints in category theory.
Limits and colimits: Two examples
Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.
Group Theory: Restriction Functor
Explores the restriction functor in group theory, focusing on its properties.
Limits and Colimits: Understanding Categories
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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.
Natural Learning Session
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Explores coproducts, universal properties, and natural transformations in category theory.
Natural Transformations in Algebra
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Explores natural transformations in algebra, defining functors and isomorphisms.
Natural Transformations
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Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.
Natural Transformations: Examples and Applications
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Explores natural transformations between functors in different categories and their applications.
Category Theory: Introduction
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Explores the concept of category theory, providing examples and discussing the opposite category concept.
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