The principal objective of this paper is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of W...The principal objective of this paper is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth category). It is shown that the canonical embedding of the old kingdom into the new kingdom preserves Weil functors.展开更多
Finite dimensional modules over Weft algebras are investigated and corresponding gauge bundle functors, from the category of vector bundles into the category of fibered manifolds, are determined. The equivalence of th...Finite dimensional modules over Weft algebras are investigated and corresponding gauge bundle functors, from the category of vector bundles into the category of fibered manifolds, are determined. The equivalence of the two definitions of gauge Well functors is proved and a number of geometric examples is presented, including a new description of vertical Well bundles.展开更多
文摘The principal objective of this paper is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth category). It is shown that the canonical embedding of the old kingdom into the new kingdom preserves Weil functors.
文摘Finite dimensional modules over Weft algebras are investigated and corresponding gauge bundle functors, from the category of vector bundles into the category of fibered manifolds, are determined. The equivalence of the two definitions of gauge Well functors is proved and a number of geometric examples is presented, including a new description of vertical Well bundles.
