3 papers
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.RT2025
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…
math.RT2024
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…