Products: Theory of Categories

Related lectures (32)

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Explores examples of categories, morphisms, groupoids, and functors in category theory.

Covers the construction and universal properties of pushouts in group theory.

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Explores the restriction functor in group theory, focusing on its properties.

Introduces functors in category theory and explains their composition.

Introduces the theory of categories through examples and discusses the product of categories.

Explores adjunctions and mutual inverses alpha and beta in category theory.

Covers morphisms with lifting properties, pushouts, pullbacks, and the uniqueness in the universal property of pushouts.

Explores how left adjoints preserve coproducts in category theory with detailed proofs and morphism diagrams.