Locally constant functors

Details Locally constant functors Locally constant functors

2008-03-30

arxiv.org/abs/0803.4342v2

Math. Proc. Camb. Phil. Soc. Volume 147 (2009), pp. 593-614

Mathematics

Algebraic Topology

Scientific paper

10.1017/S030500410900262X

We study locally constant coefficients. We first study the theory of homotopy Kan extensions with locally constant coefficients in model categories, and explain how it characterizes the homotopy theory of small categories. We explain how to interpret this in terms of left Bousfield localization of categories of diagrams with values in a combinatorial model category. At last, we explain how the theory of homotopy Kan extensions in derivators can be used to understand locally constant functors.

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