The resolving completion of an exact category

TL;DR

This paper introduces two methods to embed an exact category into a larger ambient category, one via the derived category and another through the Gabriel--Quillen embedding, focusing on resolving completions.

Contribution

It presents novel constructions of ambient categories where an exact category becomes resolving, including conditions for t-structure formation.

Findings

Construction of a pre-aisle and its orthogonal using acyclicity conditions

Necessary and sufficient conditions for the pair to form a t-structure

Application of derived and Gabriel--Quillen embeddings for resolving completion

Abstract

For an exact category we provide two constructions of an ambient category in which the initial category is resolving: In the derived category and in the Gabriel--Quillen embedding. For the first construction we describe a pre-aisle and its right orthogonal using different acyclicty conditions. We provide necessary and sufficient conditions when this pair is a t-structure.