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Related lectures (32)
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Category Theory: Introduction
Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Categories: Functors, and Natural Transformations
Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
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.
Limits and Colimits in Functor Categories
Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.
Natural Transformations
Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Category Theory: Introduction
Explores the concept of category theory, providing examples and discussing the opposite category concept.
Active Learning in Category Theory
Explores examples of categories, morphisms, groupoids, and functors in category theory.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
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.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Group Actions: G-objects in a Concrete Category
Explores G-objects in a concrete category and the framework for group actions.
Review of Simplicial Sets
Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.
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