The tangent bundle of a model category

Abstract

This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category $\mathcal{M}$ satisfying suitable conditions, we construct a relative model category $\mathcal{T}\mathcal{M}\to \mathcal{M}$, called the tangent bundle, whose fibers are models for spectra in the various over-categories of $\mathcal{M}$, and which presents the $\infty$-categorical tangent bundle. Moreover, the tangent bundle $\mathcal{T}\mathcal{M}$ inherits an enriched model structure when such a structure exists on $\mathcal{M}$. This additional structure is used in subsequent work to identify the tangent bundles of algebras over an operad and of enriched categories.

arXiv commentFormerly part of arXiv:1612.02607

References in corpus (8)

• Higher Topos Theory
• Enriched $\infty$-categories via non-symmetric $\infty$-operads
• Homology and Cohomology of E-infinity Ring Spectra
• Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
• Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes
• The abstract cotangent complex and Quillen cohomology of enriched categories
• On Reedy Model Categories
• Dwyer-Kan localization revisited

Cited by in corpus (2)

• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• Quillen cohomology of enriched operads