Lifts ans isomorphisms of commutation in bundles of jets

A linear connection or a pseudo-connection on a manifold $M$ can be considered as a generalized connection, i.e, as a (1,1)-tensor field on $TM$. In this paper we study the relationship between the lifts of $\nabla$ to $T_rM$ when $\nabla$ is considered as a connection (resp. pseudo-connection) and as a tensor field. We prove that certain isomorphims of commutation link both concepts. For this purpose, we study firstly generalized connections, obtaining some new results about them.