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A Categorical Framework for the Direct Integration of Banach Spaces
Daniel Funck, Giacomo Gavelli
Source abstract
We construct a categorical framework in which we can view the direct integral as a functor taking as input objects in a certain category of Abstract Banach bundles and outputting a Banach space. We do this by constructing a quasi-abelian category of abstract Banach bundles, and we prove certain foundational and theoretical results about this category and its objects. As a consequence, we are able to define a notion of direct integral of sheaves.
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