Invariant Definitions

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Related lectures (28)

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Endomorphisms and automorphisms of totally disconnected locally compact groups II

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Group Actions and Functors

Covers group quotient, group actions, and functors connecting sets and G-sets.

Group Theory: Adjoint Functors and G-sets

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Group Actions: Theory and Examples

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Sylow Subgroups: Structure and Properties

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.