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arXiv · 1603.00807

Categorified presheaves and sieves

Saikat Chatterjee
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Abstract

Let $\mathcal C$ be a category of a set of (small) categories. This paper concerns with the ${\mathbf {Cat}}$-valued presheaves and sieves over category $\mathcal C.$ Since ${\mathbf {Cat}}$ is not a concrete category, existing definition of presheaves can not deal with the situation. This paper proposes a new framework for the purpose. The main result is a version of Yoneda embedding for ${\mathbf {Cat}}$-valued presheaves, and construction of the ${\mathbf {Cat}}$-valued sieves over the category ${\mathcal O}(\mathbf B)$ of subcategories of a given topological category $\mathbf B.$

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Saikat Chatterjee. 2016-03-02. Categorified presheaves and sieves. https://arxiv.org/abs/1603.00807

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