We prove that any bundle functor F:ℱol → ℱℳ on the category ℱ olof all foliated manifolds without singularities and all leaf respecting maps is of locally finite order.

Let F:ℳ f →ℱℳ be a bundle functor with the point property F(pt) = pt, where pt is a one-point manifold. We prove that F is product preserving if and only if for any m and n there is an $ℱ{ℳ}_{m,n}$-canonical construction D of general connections D(Γ) on Fp:FY → FM from general connections Γ on fibred manifolds p:Y → M.