Abstract
Abstract A duchain complex of W. Dwyer and D. Kan is a common extension of the notions of a chain complex and a cochain complex. Given a square commutative diagram of duchain complexes, the lifting-extension problem asks whether there exists a diagonal map making the two resulting triangles commute. Duchain complexes have a model category structure, and hence a lift exists if the left vertical map is a cofibration, the right vertical map is a fibration, and one of them is a weak equivalence. We show that it is possible to replace the two conditions above, by a countably infinite, bigraded, family of conditions which guarantee the existence of a lift.
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