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Related lectures (26)
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Equivalence: Natural Isomorphisms and Triangular Identities
Covers the existence of natural isomorphisms and transformations with triangular identities.
Adjunctions, Products, and Coproducts
Discusses adjunctions, products, and coproducts in category theory.
Homotopical Algebra: Examples and Adjunctions
Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.
Left Adjoint Preserves Coproducts
Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.
Group Quotients: Push-out Uniqueness
Explores the uniqueness of push-outs in group quotients, focusing on specific cases and implications.
Direct Sum of Subgroups
Explores the direct sum of subgroups in an abelian group and introduces the coproduct concept in Abelian categories.
Push-out: Categorical Perspective on Quotients
Explores the concept of push-out in group homomorphisms.
Categorical Perspective: Abelian Groups
Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Direct Sums of Abelian Groups
Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.
Group Theory: Verification
Covers the verification of constructions in the context of abelian groups and Sylow subgroups.