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Related lectures (32)

Ring Theory: Sub-rings and Morphisms

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

Primary Decomposition: Understanding Schemes

Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.

Morphisms of Coverings

Covers the concept of morphisms of coverings and emphasizes the recognition of automorphisms.

Determinants: Properties and Applications

Explores the properties and applications of determinants in linear algebra.

Functor Fixed Points and Orbital Functor

Explores defining functors on morphisms, fixed points, orbits, equivariance, and composition preservation.

Functor Hom: Abelian Groups

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.

Isomorphism in Categories

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.

Products: Theory of Categories

Covers the concept of products in category theory, focusing on their properties, uniqueness, and isomorphisms.

Sheafification: Natural Procedure and Adjoints

Covers sheafification, adjoint functors, and challenges in ensuring sheaf properties.

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