Quotient Groups and Push-outs

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

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Introduces the basics of group theory, defining groups, categories, and groupoids.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.