Two-term silting and $\ddot{I}„$-cluster morphism categories

Abstract

We generalise $\ddot{I}„$-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 $\ddot{I}„$-tilting reduction will be an essential ingredient when linking our definition to those of Buan--Marsh and Buan--Hanson.

35 pages. v3: §2, which previously included a flawed definition, has been removed, §2 (previously §3) considerably reshaped. v4: Thm. 5.3 has been removed. Contact information updated. v5: Setting generalised to non-positive dg algebras with finite dimensional cohomology in all degrees, Section 5 removed, substantial additions to some proofs