On the factor-web $\overline W(\rho,r,r)$ of the three-web $W(r,r,r)$

The notion of the factor-web $\overline W(\rho,r,r)$ ($1\leq\rho<r$) is defined for the three-web $W(r,r,r)$ formed on a $2r$-dimensional differentiable manifold by three $r$-dimensional smooth foliations. Embedding of the factor-web in the initial web $W(r,r,r)$ is constructed. This construction is a well-known geometric analog of the canonical extension of a Lie group of transformations to its parameter group.