4 papers
Complex Matching Distance and Stability for Minimal Projective Resolutions, with Applications to Persistence
Hideto Asashiba, Amit K. Patel
We develop a stability theory for minimal projective resolutions of -modules, where is a finite metric poset. We use the Gülen-McCleary distance on $\math…
-Stability of Weighted Persistence Diagrams
Aziz Burak Gülen, Facundo Mémoli, Amit Patel
We introduce the concept of weighted persistence diagrams and develop a functorial pipeline for constructing them from finite metric measure spaces. This builds upon an existing fu…
Möbius Homology
Amit Patel, Primoz Skraba
This paper introduces and develops Möbius homology, a homology theory for representations of finite posets into abelian categories. Although the connection between poset topology…
A Categorical Approach to Möbius Inversion via Derived Functors
Alex Elchesen, Amit Patel
We develop a cohomological approach to Möbius inversion using derived functors in the enriched categorical setting. For a poset and a closed symmetric monoidal abelian categor…