Weight structures cogenerated by weak cocompact objects

TL;DR

This paper investigates t-structures and weight structures in triangulated categories generated by objects with weaker conditions than compactness, revealing their relationships under certain hypotheses.

Contribution

It introduces a framework for weight and t-structures cogenerated by weakly cocompact objects and explores their adjacency relationships.

Findings

Weight structures are right adjacent to t-structures under specific conditions.

The study extends the understanding of structures generated by non-compact objects.

Conditions weaker than compactness can still produce meaningful structural relationships.

Abstract

We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. We also study weight structures cogenerated by sets of objects satisfying the dual condition. Under some appropriate hypothesis, it turns out that the weight structure is right adjacent to the t-structure.