Two-term silting and $\tau$-cluster morphism categories

TL;DR

This paper extends the concept of $ au$-cluster morphism categories to non-positive dg algebras with finite-dimensional cohomology, exploring their structural properties and connections to existing theories.

Contribution

It generalizes $ au$-cluster morphism categories to a broader algebraic setting involving non-positive dg algebras with finite-dimensional cohomology.

Findings

Established compatibility of silting reduction with support $ au$-tilting reduction

Linked new definitions to existing cluster theories

Extended the framework of $ au$-cluster categories

Abstract

We generalise $\tau$-cluster morphism categories to the setting of non-positive dg algebras with finite dimensional cohomology in all degrees. The compatibility of silting reduction with support $\tau$-tilting reduction will be an essential ingredient when linking our definition to those of Buan--Marsh and Buan--Hanson.