DUALITY FOR BASE-CHANGING MORPHISMS OF VECTOR-BUNDLES, MODULES, LIE ALGEBROIDS AND POISSON STRUCTURES

The main result of this paper is an extension to Poisson bundles [4] a nd Lie algebroids of the classical result that a linear map of Lie alg ebras is a morphism of Lie algebras if and only if its dual is a Poiss on morphism. In formulating this extension we introduce a second class of structural maps for vector bundles, which we call comorphisms, alo ngside the standard morphisms, and we further show that this concept o f comorphism, in conjunction with a corresponding concept for modules, allows one to extend to arbitrary base-changing morphisms of arbitrar y vector bundles the familiar duality and section functors which are n ormally defined only in the base-preserving case.