24 citations · 96 across the 30 of their papers we have counts for
28 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…
Positive and negative extensions in extriangulated categories
Mikhail Gorsky, Hiroyuki Nakaoka, Yann Palu
We initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We show tha…
Localization of extriangulated categories
Hiroyuki Nakaoka, Yasuaki Ogawa, Arashi Sakai
In this article, we show that the localization of an extriangulated category by a multiplicative system satisfying mild assumptions can be equipped with a natural, universal struct…
External triangulation of the homotopy category of exact quasi-category
Hiroyuki Nakaoka, Yann Palu
Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a…
Auslander--Reiten theory in extriangulated categories
Osamu Iyama, Hiroyuki Nakaoka, Yann Palu
The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories. In this article, we develop Ausland…