Flow does not model flows up to weak dihomotopy
Algebraic Topology
2021-08-24 v3 Category Theory
Abstract
We prove that the category of flows cannot be the underlying category of a model category whose corresponding homotopy types are the flows up to weak dihomotopy. Some hints are given to overcome this problem. In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable version of the category of flows.
Keywords
Cite
@article{arxiv.math/0404328,
title = {Flow does not model flows up to weak dihomotopy},
author = {Philippe Gaucher},
journal= {arXiv preprint arXiv:math/0404328},
year = {2021}
}
Comments
v2 16 pages, 3 figures ; updated bibliography + slight improvements and corrections of typos ; v3 only the Journal-ref field