Semibricks and wide subcategories in extended module categories

2025/11/11 by Esha Gupta, Zhou Yu, Gupta, Esha +1
Mathematics · #16E35 #16G10 #18G80 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2511.08157

openalex publication_date 2025/11/11 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28

Abstract

For d≥ 1, we define semibricks and wide subcategories in the d-extended hearts of bounded t-structures on a triangulated category. We show that these semibricks are in bijection with finite-length wide subcategories. When the d-extended heart is the d-extended module category d-modΛ of a finite-dimensional algebra Λ over a field, we define left/right-finite semibricks and left/right-finite wide subcategories in d-modΛ and show bijections with (d+1)-term simple-minded collections, generalising the bijections between 2-term simple-minded collections, left/right-finite wide subcategories and left/right-finite semibricks in modΛ. We use a relation between semibricks and silting complexes to characterise which mutations of (d+1)-term silting complexes are again (d+1)-term.

Citations

• On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras
• Tilting theory for extended module categories
• On d-term silting objects, torsion classes, and cotorsion classes
• On thick subcategories of the category of projective presentations
• Hereditary cotorsion pairs and silting subcategories in extriangulated categories
• Intervals of s-torsion pairs in extriangulated categories with negative first extensions
• Co-t-structures, cotilting and cotorsion pairs
• Positive Fuss-Catalan numbers and Simple-minded systems in negative Calabi-Yau categories
• Semibricks
• Silting objects, simple-minded collections, t-structures and co-t-structures for finite-dimensional algebras
• Weight structures and simple dg modules for positive dg algebras
• General Presentations of Algebras
• Exact Categories
• Auslander-Reiten triangles in subcategories

Related

• Semibricks in extriangulated categories
• Classifying subcategories of modules
• AIR tilting subcategories of extended hearts
• Semibricks
• Wide subcategories and brick-finiteness for length categories