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We study the prolongation of various geometric structures on a fibered manifold with respect to the Weil functor T A or a fiber product preserving bundle functor F on the category of all fibered manifolds with m-dimensional bases and their morphisms with local diffeomorphisms as base maps. Special attention is paid to connections, vector bundles, principal bundles and weak principal bundles.doi:10.18514/mmn.2013.903 fatcat:ezm73trvovd3xkhzrlkvzhq7da