Multilinear Map

Let A i subscript 𝐴 𝑖 A_{i} be a family of Abelian Groups. A multilinear map A i → B → subscript 𝐴 𝑖 𝐵 A_{i}\to B is a function A i → B → subscript 𝐴 𝑖 𝐵 A_{i}\to B that is a group homomorphism in each A i subscript 𝐴 𝑖 A_{i} separately.

Relation to Joint Category Theory question

Is there a relation to Joint Category Theory?