On the geometry of smooth mappings of $ R ^ {q} \ times R ^ {p} \ rightarrow R ^ {\ lambda} $, generalizing groups

The notions of associativity was generalized by author in [7], [10] for smooth functions, where the dimensions $x,y,z$ are different. In this paper for smooth grouppoids we introduce a nontrivial analogue for commutative Li groups and we establish equations for corresponding multidimensional three-web.