4 papers
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…
The index in -exact categories
Francesca Fedele, Peter Jørgensen, Amit Shah
Starting from its original definition in module categories with respect to projective modules, the index has played an important role in various aspects of homological algebra, cat…
The index with respect to a contravariantly finite subcategory
Francesca Fedele, Peter Jorgensen, Amit Shah
Cluster algebras are categorified by cluster categories, and -vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently…
A resolution theorem for extriangulated categories with applications to the index
Yasuaki Ogawa, Amit Shah
Quillen's Resolution Theorem in algebraic -theory provides a powerful computational tool for calculating -groups of exact categories. At the level of , this result goes…