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Lecture
Categories and Functors: An Introduction
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Related lectures (32)
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Simplicial and Cosimplicial Objects: Examples and Applications
Covers simplicial and cosimplicial objects in category theory with practical examples.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
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.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Active Learning: Functors and Geometric Realization
Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.
Natural Transformations: Examples and Applications
Explores natural transformations between functors in different categories and their applications.
Natural Learning Session
Explores coproducts, universal properties, and natural transformations in category theory.
Category Theory: G-sets and Left Adjoint Functor
Explores the construction of G-sets and left adjoint functors in category theory.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
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: Functors
Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Active Learning in Category Theory
Explores examples of categories, morphisms, groupoids, and functors in category theory.
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