Fibrantly-transferred model structures

Abstract

We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of the classical right-transfer theorem in the presence of an adjunction. Namely, instead of lifting the classes of fibrations and weak equivalences through the right adjoint, we now only do so between fibrant objects, which allows for a wider class of applications.

Fixed a mistake in the construction of the model structures in sections 5-6 of v1; the revised versions now appear as part of the paper "Double categorical equivalences" (arXiv:2509.23181). Final version to appear in Transactions of the AMS