Fibrantly-transferred model structures

TL;DR

This paper introduces a flexible method for constructing model structures in homotopy theory, broadening the classical transfer theorem by focusing on fibrant objects and weak equivalences.

Contribution

It presents a new technique for transferring model structures that relaxes the traditional lifting conditions, enabling more applications in homotopical algebra.

Findings

Developed a generalized transfer theorem for model structures.

Extended the classical right-transfer theorem with fewer restrictions.

Demonstrated broader applicability in constructing model categories.

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.