Locally constant functors

Abstract

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.

References in corpus (3)

• Cofibrations in Homotopy Theory
• On (Enriched) Left Bousfield Localization of Model Categories
• Parametrized spaces model locally constant homotopy sheaves

Cited by in corpus (11)

• Homotopy theory for algebras over polynomial monads
• Homotopy theory of algebraic quantum field theories
• Morita cohomology
• Quantum field theories on categories fibered in groupoids
• Left Bousfield localization without left properness
• Bousfield Localization and Eilenberg-Moore Categories
• Polynomial functors in manifold calculus
• Derived sections of Grothendieck fibrations and the problems of homotopical algebra
• Unbounded Algebraic Derivators
• An extension of Quillen's Theorem B
• Monoidal Properties of Franke's Exotic Equivalence