Andrew Stacey

Andrew Stacey
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By: Andrew Stacey
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Andrew Stacey

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Mon, 17th Dec 2007 (Research :: Preprints)

On Categories of Smooth Objects (PDF or PS)

New version: fairly comprehensively rewritten.

We compare various different definitions of the category of smooth objects. The definitions compared are due to Chen, Frölicher, Sikorski, Smith, and Souriau. The purpose of the comparison is to answer two questions: which, if any, captures the essence of smoothness? and how are the various categories related to each other? The first is a subjective question and we give a subjective answer: Frölicher spaces. For the second we give a more objective answer in terms of the existence of functors between the categories with certain nice properties, such as the existence of inverses and of adjunctions. We also make some general remarks about the role that topology does or doesn't play and on how one might go about defining tangent and cotangential structures on Frölicher spaces.

  • In a 2-up version as PDF or PS
  • In a 1-up version as PDF or PS (be tree-friendly: if you must print, print the 2-up version double-sided).
  • On the arxiv as 0802.2225.
  • Discussion on the n-Category Café as Comparative Smootheology (and continuing in other entries linked from that one).

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Wed, 29th Apr 2009