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Two-term silting and $τ$-cluster morphism categories

Erlend D. Børve

Abstract

We generalise $τ$-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 $τ$-tilting reduction will be an essential ingredient when linking our definition to those of Buan--Marsh and Buan--Hanson.

Two-term silting and $τ$-cluster morphism categories

Abstract

We generalise -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 -tilting reduction will be an essential ingredient when linking our definition to those of Buan--Marsh and Buan--Hanson.

Paper Structure

This paper contains 7 sections, 27 theorems, 71 equations.

Table of Contents

  1. Introduction
  2. Notation and preliminaries
  3. t-structures and wide subcategories of the heart
  4. Silting and $\tau$-tilting
  5. Silting t-structures and reduction
  6. Compatibility of the Iyama--Yang and Buan--Marsh bijections
  7. $\tau$-cluster morphism categories

Key Result

Proposition 1.4

Let $\mathcal{D}$ be a triangulated category equipped with a t-structure $(\mathcal{D}^{\leq 0},\mathcal{D}^{>0})$.

Theorems & Definitions (53)

  • Definition 1.1
  • Remark 1.2
  • Remark 1.3
  • Proposition 1.4
  • Definition 1.5: BBD82
  • Remark 1.6
  • Proposition 1.7: BBD82
  • Lemma 1.8
  • proof
  • Lemma 1.9
  • ...and 43 more