A new approach to projectivity in the categories of complexes, II

TL;DR

This paper extends the concept of subprojectivity from modules to complexes, unifying classical results and providing examples to illustrate the scope and limitations of these generalized notions.

Contribution

It generalizes the subprojectivity framework to complexes, unifying classical results and characterizing subprojectivity via homotopy category morphisms.

Findings

Subprojectivity of complexes can be characterized in terms of homotopy category morphisms.

The paper provides examples illustrating the scope and limits of the generalized results.

Unification of classical projectivity and flatness concepts in the context of complexes.

Abstract

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying several known classical results. We further provide various examples to illustrate the scopes and limits of the established results. This paper is a continuation of a recent work in which it was shown among other several things that the subprojectivity of complexes can be characterized in terms of morphisms in the homotopy category.