The tangent bundle of a model category

Autor: Harpaz, Yonatan, Nuiten, Joost, Prasma, Matan
Rok vydání: 2018
Předmět:
Druh dokumentu: Working Paper
Popis: 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 $\mathcal{TM} \to \mathcal{M}$, 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 $\mathcal{TM}$ 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.
Comment: Formerly part of arXiv:1612.02607
Databáze: arXiv