Abstract

AbstractThe complete description is given of the product preserving gauge bundle functors F on the category of double vector bundles in terms of the ‐bilinear maps , where are Weil algebras and are finite dimensional (over ) ‐modules. Then the so‐called “iteration” problem is solved (i.e. by means of and is computed). That any two product preserving gauge bundle functors on commute is derived. All gauge natural operators lifting double linear vector fields to product preserving gauge bundle functors F are completely described.

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