Abelian 2-group
In mathematics, an Abelian 2-group is a higher dimensional analogue of an Abelian group, in the sense of higher algebra, which were originally introduced by Alexander Grothendieck while studying abstract structures surrounding Abelian varieties and Picard groups. More concretely, they are given by groupoids A {\displaystyle \mathbb {A} } which have a bifunctor + : A × A → A {\displaystyle +:\mathbb {A} \times \mathbb {A} \to \mathbb {A} } which acts formally like the addition an Abelian group.