Proof of Existence

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Pushouts in Group Theory: Universal Properties Explained

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

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.

Group Theory: Restriction Functor

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

Construction of Alpha and Beta

Covers the construction of alpha and beta in group theory, emphasizing commutativity and natural transformations.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Functor Hom: Abelian Groups

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

Active Learning: Functors and Geometric Realization

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.