Characterizations of abstract stable homotopy theories
Algebraic Topology
2016-02-25 v1 Category Theory
Representation Theory
Abstract
In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a derivator is stable if and only if homotopy finite limits and homotopy finite colimits commute, and there are variants for sufficiently finite Kan extensions. As an additional reformulation, a derivator is stable if and only if it admits a zero object and if partial cone and partial fiber morphisms commute on squares.
Keywords
Cite
@article{arxiv.1602.07632,
title = {Characterizations of abstract stable homotopy theories},
author = {Moritz Groth},
journal= {arXiv preprint arXiv:1602.07632},
year = {2016}
}