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Homotopy theory of small diagrams over large categories

Boris Chorny·William G. Dwyer
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Abstract

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the category of simplicial sets which satisfy a stronger universal property than the customary homotopy localization functors do.

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Boris Chorny, William G. Dwyer. 2006-07-05. Homotopy theory of small diagrams over large categories. https://arxiv.org/abs/math/0607117

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