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Lecture
Adjunctions, Products, and Coproducts
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Related lectures (32)
Natural Learning Session
Explores coproducts, universal properties, and natural transformations 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.
Natural Transformations: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Functors and Adjunctions
Explores functors between categories and the conditions for left and right adjoints.
Adjunctions and Functor Categories: Exploring Connections
Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.
Categories and Functors
Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.
Limits and Colimits in Functor Categories
Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.
Left Adjoint Preserves Coproducts
Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.
Categories and Functors: An Introduction
Provides an overview of categories, functors, and natural transformations in mathematics.
Functors and Natural Transformations
Delves into functors, natural transformations, and group actions with explicit examples.
Active Learning Session
Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.
Homotopical Algebra: Examples and Adjunctions
Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.
Natural Transformations
Explores natural transformations between functors, emphasizing their composition-preserving properties and significance 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.
Active Learning in Category Theory
Explores examples of categories, morphisms, groupoids, and functors in category theory.
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.
Isomorphism in Categories
Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.
Group Theory: Adjoint Functors and G-sets
Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.
An Introduction to Category Theory: Products and Coproducts
Demonstrates how adjoints preserve coproducts and products in category theory.
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