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Lecture
Adjunctions, Products, and Coproducts
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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.