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arXiv · 1411.5526

Model structures for coalgebras

Gabriel C. Drummond-Cole·Joseph Hirsh
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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.

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Gabriel C. Drummond-Cole, Joseph Hirsh. 2014-11-20. Model structures for coalgebras. https://arxiv.org/abs/1411.5526

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