EN
Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some "special" fibred coordinate systems on Y, and then we construct a general connection $\widetilde{ℱ}(Γ,∇)$ on Fp:FY → FM for any vector bundle functor F: ℳ f → 𝓥𝓑 of finite order.