Anna Montaruli: Injective Abelian groups in constructive Mathematics

Abstract:
It is well-known that in the classical setting an Abelian group is injective if and only if it is divisible. The prove of this fact uses Zorn’s Lemma, which we know to be equivalent, under certain conditions, to the Axiom of Choice (AC). How things would change if we work without AC? In this talk I’ll present an intermediate result that goes in this direction: The existence of a non trivial discrete injective object in the category Ab of Abelian groups implies the Weak Law of Excluded Middle (WLEM).