Fibrantly-transferred model structures
Léonard Guetta, Lyne Moser, Maru Sarazola, Paula Verdugo
TL;DR
The paper addresses the challenge of constructing model-categorical structures in categories related to a known model category via adjunctions. It develops techniques to build model structures from a prescribed class of cofibrations, a fibrant-object class, and a weak equivalences class, and specializes to a right-transfer variant that transfers data between fibrant objects. The main contribution is a more flexible transfer principle that relaxes the requirement of lifting through the right adjoint to a transfer between fibrant objects, expanding applicability to new settings. This work enhances the homotopical toolbox for derived functors and comparisons in categories where fibrant-object data is more accessible, broadening practical use in homotopical algebra and algebraic topology.
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.