Tensor structures in the theory of modulus presheaves with transfers

The tensor product of $${\mathbb {A}}^1$$ -invariant sheaves with transfers introduced by Voevodsky is generalized to reciprocity via the theory modulus presheaves transfers. We prove several general properties this construction and compute it in some cases. In particular we obtain new (motivic) presentations absolute Kähler differentials first infinitesimal neighborhood diagonal.