# Homological properties of modules with finite weak injective and weak flat dimensions

## TL;DR

This paper introduces new relative derived functors based on weak flat resolutions to analyze modules' weak flat dimensions, explores larger classes of modules, and studies their covers and preenvelopes for broader homological insights.

## Contribution

It defines a novel class of relative derived functors and investigates larger module classes, extending the understanding of weak injective and flat modules.

## Key findings

- Defined new relative derived functors for weak flat dimensions
- Studied existence of covers and preenvelopes for larger module classes
- Provided applications of the theoretical framework

## Abstract

In this paper, we define a class of relative derived functors in terms of left or right weak flat resolutions to compute the weak flat dimension of modules. Moreover, we investigate two classes of modules larger than that of weak injective and weak flat modules, study the existence of covers and preenvelopes, and give some applications.