The purpose of this chapter is to develop a general framework for the theory of geometric objects and operators and to reduce local geometric considerations to finite order problems. In general, the latter is a hard analytical problem and its solution essentially depends on the category in question. Roughly speaking, our methods are efficient when we deal with a sufficiently large class of smooth maps, but they fail e.g. for analytic maps.
KeywordsVector Bundle Natural Transformation Finite Order Natural Operator Smooth Action
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