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Related lectures (30)
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Two Definitions of Group Action
Explores two definitions of group action and their equivalence through bijection in group homomorphisms.
Isometries and Group Homomorphisms
Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.
Group Actions: G-object Notion
Explores the categorical framework for group actions, focusing on the concept of G-objects in different categories.
Categorical Perspective: Abelian Groups
Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Abelian Groups: Category Theory
Explores the concept of abelian groups and their group homomorphisms.
Linear Transformations: Dimension Theorems
Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.
Symmetric Group: Cycle Notation
Explores the symmetric group, emphasizing cycle notation and group properties.
Endomorphisms: Matrix Equivalence
Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.
Cohomology Groups: Hopf Formula
Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.
Epsilonization: Algebra Homomorphisms and Derivation Numbers
Covers algebra homomorphisms, derivation numbers, and closed subvariety concepts in epsilonization.
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