8 citations · 30 across the 12 of their papers we have counts for
12 papers
On reachability categories, persistence, and commuting algebras of quivers
Luigi Caputi, Henri Riihimäki
For a finite quiver , we study the reachability category . We investigate the properties of from both a categorical and a topological viewpo…
From the Mayer-Vietoris spectral sequence to überhomology
Luigi Caputi, Daniele Celoria, Carlo Collari
We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexe…
On finite generation in magnitude (co)homology, and its torsion
Luigi Caputi, Carlo Collari
The aim of this paper is to apply the framework, which was developed by Sam and Snowden, to study structural properties of graph homologies, in the spirit of Ramos, Miyata and Prou…
On the homotopy type of multipath complexes
Luigi Caputi, Carlo Collari, Sabino Di Trani +1
A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph is the simplicial complex whose faces are the multipaths of ${\tt…
Hochschild homology, and a persistent approach via connectivity digraphs
Luigi Caputi, Henri Riihimäki
We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree . To extend…
Monotone cohomologies and oriented matchings
Luigi Caputi, Daniele Celoria, Carlo Collari
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs,…
Categorifying connected domination via graph überhomology
Luigi Caputi, Daniele Celoria, Carlo Collari
Überhomology is a recently defined homology theory for simplicial complexes, which yields subtle information on graphs. We prove that bold homology, a certain specialisation of übe…
Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
Luigi Caputi, Carlo Collari, Sabino Di Trani
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path pos…
Multipath cohomology of directed graphs
Luigi Caputi, Carlo Collari, Sabino Di Trani
This work is part of a series of papers focusing on multipath cohomology of directed graphs. Multipath cohomology is defined as the (poset) homology of the path poset -- i.e., the…
Cyclic homology for bornological coarse spaces
Luigi Caputi
We define Hochschild and cyclic homologies for bornological coarse spaces: for a fixed field and group , these are lax symmetric monoidal functors and…
Controlled objects as a symmetric monoidal functor
Ulrich Bunke, Luigi Caputi
The goal of this paper is to associate functorially to every symmetric monoidal additive category with a strict -action a lax symmetric monoidal functor $\mathbf{V}…
Localization for coarse homology theories
Ulrich Bunke, Luigi Caputi
We introduce the notion of a Bredon-style equivariant coarse homology theory. We show that such a Bredon-style equivariant coarse homology theory satisfies localization theorems an…