On homotopy varieties
Category Theory
2007-05-23 v2 Algebraic Topology
Abstract
Given an algebraic theory , a homotopy -algebra is a simplicial set where all equations from hold up to homotopy. All homotopy -algebras form a homotopy variety. We give a characterization of homotopy varieties analogous to the characterization of varieties. We will also study homotopy models of limit theories which leads to homotopy locally presentable categories. These were recently considered by Simpson, Lurie, To\"{e}n and Vezzosi.
Cite
@article{arxiv.math/0509655,
title = {On homotopy varieties},
author = {J. Rosicky},
journal= {arXiv preprint arXiv:math/0509655},
year = {2007}
}
Comments
Proposition 4.5 is not valid; see Remark 4.5(e) in the new version. All other results are correct but there are gaps in proofs. They are fixed by reducing simplicial categories to fibrant ones and replacing homotopy colimits by fibrant ones, as well