English

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.

Keywords

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

R2 v1 2026-06-22T07:05:47.989Z