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This paper studies the homotopy theory of parametrized spectrum objects in a model category from a global point of view. More precisely, for a model category $M$ satisfying suitable conditions, we construct a map of model categories $TM \to M$, called the tangent bundle, whose fiber over an object in $M$ is a model category for spectra in its over-category. We show that the tangent bundle is a relative model category and presents the $\infty$-categorical tangent bundle, as constructed by Lurie. Moreover, the tangent bundle $TM$ inherits an enriched model structure from $M$. This additional structure is used in subsequent work to identify the tangent bundles of algebras over an operad and of enriched categories, but may be of independent interest.
@article{TAC_2019_34_a32,
author = {Yonatan Harpaz and Joost Nuiten and Matan Prasma},
title = {The tangent bundle of a model category},
journal = {Theory and applications of categories},
pages = {1039--1072},
publisher = {mathdoc},
volume = {34},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a32/}
}
Yonatan Harpaz; Joost Nuiten; Matan Prasma. The tangent bundle of a model category. Theory and applications of categories, Tome 34 (2019), pp. 1039-1072. http://geodesic.mathdoc.fr/item/TAC_2019_34_a32/