7 papers
Extended heart construction (I): The heart of -cotorsion pairs on triangulated categories
Nao Mochizuki, Hiroyuki Nakaoka, Yasuaki Ogawa
The heart of a -structure and the ideal quotient by a cluster tilting subcategory are classical constructions that produce abelian categories from triangulated categories. Their…
Extended Module Categories in Higher Cluster Tilting Theory
Nao Mochizuki
In this paper, we study ideal quotients of triangulated categories by higher cluster tilting subcategories. Koenig and Zhu proved that the ideal quotient by a -cluster tilting s…
Higher exact dg-categories
Nao Mochizuki, Hiroyuki Nakaoka
We introduce the notion of an -exact dg-category. This notion provides a higher analogue of Chen's exact dg-category, in the sense that the case where equals 1 recovers exac…
Auslander correspondence for proper connective DG-algebras via extended module categories
Nao Mochizuki
We establish a -dimensional Auslander correspondence for -truncated proper connective DG-algebras via -extended module categories. A -truncated proper connective DG-alg…
An enhanced extriangulated subquotient
Nao Mochizuki, Yasuaki Ogawa
Bondal-Kapranov's notion of enhanced triangulated categories behaves well in the framework of localization theory, in the sense that the Verdier quotient of triangulated categories…
Higher-dimensional generalization of abelian categories via DG-categories
Nao Mochizuki
In this paper, we introduce abelian -truncated DG-categories as an -dimensional analogue of abelian categories in the setting of DG-categories. When , this recovers ordi…