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Selective Categories and Linear Canonical Relations
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Journal Article
Selective Categories and Linear Canonical Relations
2014
Overview
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are ''good''. We then apply this notion to the category [...] of linear canonical relations and the result [...] of our version of the WW construction, identifying the morphisms in the latter with pairs [...] consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in [...] itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts. [ProQuest: [...] denotes formulae omitted.]
Publisher
National Academy of Sciences of Ukraine
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