Lectures related to Quotient Groups and Push-outs

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.

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

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

Explores direct sums in group theory, focusing on abelian groups and their implications.

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Explores group operations with cyclic properties and the universal ownership of quotients.

Covers the concepts of torsion and divisibility in group theory.

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Explores the uniqueness of push-outs in group quotients, focusing on specific cases and implications.

Introduces subgroups and homomorphisms in group theory, with examples for illustration.