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Categories and Functors
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Related lectures (32)
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Limits and colimits in Top
Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Functors: Categories, Functors, and Natural Transformations
Introduces functors, including identity and forgetful functors, and explores duality functors.
Natural Transformations: Categories, Functors, and Equivalence
Covers natural transformations between functors, identity transformations, and equivalence of categories.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
Isomorphism in Categories
Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
