On derived equivalences for categories of generalized intervals of a finite poset

TL;DR

This paper investigates two related constructions on finite posets, demonstrating their equivalence at the derived category level, which advances understanding of their algebraic and categorical properties.

Contribution

It establishes an equivalence between two different constructions related to intervals in finite posets at the derived category level.

Findings

The two constructions are equivalent in derived categories.

The second construction involves a poset with additional zero-relations.

Main result links the algebraic structures of the two constructions.

Abstract

We study two constructions related to the intervals of finite posets. The first one is a poset. The second one is more complicated. Loosely speaking it can be seen as a poset with some extra zero-relations. As main result, we show that these two constructions are equivalent at the level of derived categories.