3 papers
math.CT2026
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…
math.KT2026
Weak Waldhausen categories and a localization theorem
Yasuaki Ogawa, Amit Shah
Waldhausen categories were introduced to extend algebraic -theory beyond Quillen's exact categories. In this article, we modify Waldhausen's axioms so that it matches better wit…
math.CT2025
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…