3 papers
math.AT2026
Choosing the Geometry: valuations, norms, and contours
Jens Agerberg, Wojciech Chachólski, Christina Kapatsori
We develop a general framework for constructing pseudometrics on objects of Abelian categories using valuations, which assign non-negative costs to morphisms. Specializing to finit…
math.AT2024
Realisations of posets and tameness
Wojciech Chacholski, Alvin Jin, Francesca Tombari
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we de…
math.AT2024
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…