4 papers · 1 filter
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…
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…
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…