Fibrations and cofibrations in a stratified model category

Abstract

We introduce $n$-acyclic cofibrations and $n$-acyclic fibrations in a stratified model category and show that they have the key properties of (acyclic) cofibrations and (acyclic) fibrations in a model category. We analyse their action on sets of homotopy classes and give an application to homotopy colimits and limits.