Lecture
This lecture covers the construction of the free abelian group, denoted FAb(X), as the direct sum of elements from a set X. The definition extends to a functor FAb: Ens → Ab, which is the left adjoint of the forgetful functor U: Ab → Ens. Important cases and properties of the free abelian group are discussed, including its relationship with categorical constructions in Ab. The lecture concludes with the introduction to the Hom functor, setting the stage for further exploration.