Cat-valued sheaves

Saikat Chatterjee ()
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Saikat Chatterjee: Indian Institute of Science Education and Research

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 3, 451-503

Abstract: Abstract Let $$\mathcal{\widetilde{O}}$$ O ~ (B) be the category of (open) subcategories of a topological groupoid B: In this paper we study Cat-valued sheaves over category $$\mathcal{\widetilde{O}}$$ O ~ (B): The paper introduces a notion of categorical union, such that the categorical union of subcategories is a subcategory. We use this definition of categorical unions to define a categorical cover of a topological category. Instead of assuming a Grothendieck topology, we define Cat-valued sheaves in terms of the categorical cover defined in this paper. The main result is the following. For a fixed category C, the categories of local functorial sections from B to C define a Catvalued sheaf on $$\mathcal{\widetilde{O}}$$ O ~ (B): Replacing C with a categorical group G; we find a CatGrp-valued sheaf on $$\mathcal{\widetilde{O}}$$ O ~ (B): We also relate and distinguish our construction with the notion of stacks.

Keywords: Presheaves; sheaves; union of subcategories; categorical groups (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0279-2

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