Model structures for coalgebras

Geometry Topology Seminar
Monday, February 2, 2015 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
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.