Covariant & Contravariant Homotopy Theories
Category Theory
2019-08-20 v1
Abstract
Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on simplicial sets as well as the coCartesian and Cartesian model structures on marked simplicial sets are examples of our formalism. In this setting, notions of final and initial maps and smooth and proper maps arise very naturally and we will identify these maps in the examples.
Keywords
Cite
@article{arxiv.1908.06879,
title = {Covariant & Contravariant Homotopy Theories},
author = {Hoang Kim Nguyen},
journal= {arXiv preprint arXiv:1908.06879},
year = {2019}
}
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29 pages