Group Quotients: Push-out Uniqueness

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Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Quotient Groups and Push-outs

Covers the construction of push-outs in the category Ens and philosophical concepts of universality and co-universality.

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.

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Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Universal Property of G*H

Covers the universal property of group products and homomorphisms through quotients, with examples.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.