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Full and faithful functors
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Related lectures (32)
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Homotopical Algebra: Examples and Adjunctions
Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.
Adjunctions and Limits: Exploring Functors and Co-limits
Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Divisibility and Torsion
Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.
Functors: Categories, Functors, and Natural Transformations
Introduces functors, including identity and forgetful functors, and explores duality functors.
Group Actions: G-objects in a Concrete Category
Explores G-objects in a concrete category and the framework for group actions.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Functors and Adjunctions
Explores functors between categories and the conditions for left and right adjoints.
Hom Functor: Abelian Groups
Explores the Hom functor for abelian groups and its relation to direct sums.
Active Learning: Products and Categories
Discusses the properties of products in categories and their relationship with small and arbitrary categories.
Functor Categories Composition and Induced Functors
Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.
Transfer of Model Structures
Covers the transfer of model structures through adjunctions in the context of model categories.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Free Abelian Group: Construction and Properties
Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.
Functor Hom: Abelian Groups
Explores the Hom functor in Abelian groups, focusing on its construction and properties.
Natural Examples of Simplicial Sets
Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.
Homological Algebra: Exact Sequences
Covers exact sequences in homological algebra and the properties of Hom functors.
Group Operations and Homomorphisms in Abelian Groups
Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.
Free Action Functor: Left Adjoint to Forgetful Functor
Explores the free action functor as the left adjoint to the forgetful functor, emphasizing its equivalence-preserving properties and natural bijection.
Construction of Free Action Functor
Explores the construction of the free action functor in group theory and category theory, emphasizing group actions and their properties.
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