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Categories and Functors
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Related lectures (32)
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Functors: Categories, Functors, and Natural Transformations
Introduces functors, including identity and forgetful functors, and explores duality functors.
Functor Categories Composition and Induced Functors
Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Natural Transformations Composition
Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Lifting properties and model categories
Covers the study of lifting properties in categories, focusing on the left and right lifting properties.
Adjunction between Simplicial Sets and Enriched Categories
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
Limits and colimits: Concrete Examples
Explores concrete examples of limits and colimits in functors and different categories.