Model structures for coalgebras
Algebraic Topology
2015-05-26 v2 Category Theory
Abstract
Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphism on homology. In the other, the weak equivalences are maps which induce a weak equivalence of algebras under the cobar functor. We unify these two approaches, realizing them as the two extremes of a partially ordered set of model category structures on coalgebras over a cooperad satisfying mild conditions.
Cite
@article{arxiv.1411.5526,
title = {Model structures for coalgebras},
author = {Gabriel C. Drummond-Cole and Joseph Hirsh},
journal= {arXiv preprint arXiv:1411.5526},
year = {2015}
}
Comments
14 pages. Version accepted for publication in Proc. Amer. Math. Soc