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Related lectures (32)
Functors and Adjunctions
Explores functors between categories and the conditions for left and right adjoints.
Functors: Categories, Functors, and Natural Transformations
Introduces functors, including identity and forgetful functors, and explores duality functors.
Functor Categories: (Co)Limits and Simplicial Sets
Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.
Functor Categories Composition and Induced Functors
Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.
Natural Transformations Composition
Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Limits and colimits: Introduction, Chapter 1(c)
Introduces limits and colimits in a category, covering their properties and uniqueness.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
Functors: Examples
Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.
Invariant Definitions
Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.
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.
Introduction to Category Theory: Natural Transformations
Covers the concept of natural transformations between functors and their associativity.
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