Lectures related to Group Theory Fundamentals

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

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

Covers the construction of R and equivalence relations in sequences and linear recurrences.

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

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Explores independence in infinite coin tosses, covering sets, shifts, and T-invariance.

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.

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