2 citations · 5 across the 10 of their papers we have counts for
5 papers · 1 filter
Persistent Magnitude Homology for Quantitative Equational Theories
Luciano Melodia
A quantitative equational theory reasons about terms that agree up to a numerical error. It presents a free algebra over a metric space of generators, the terms of t…
Learning Transfers: Kan Extensions of Topological Invariants of Learned Representations
Luciano Melodia
When a learned representation is reused for a new task, which of its structure should survive? A task is a small category, a change of task is a functor , and the invariants of…
Universal Coefficients and Mayer-Vietoris Sequence for Groupoid Homology
Luciano Melodia
We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let be a topological abelian group. For set $C_n(\mathcal G;A) := C_c(\mat…
Discrete Coefficients and Open Invariant Covers in the Homology of Ample Groupoids
Luciano Melodia
The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve. Two hypotheses routinely imposed on this complex behave in…
Groupoid Homology and Classifying-Space Homology Are Not Isomorphic
Luciano Melodia
For an ample groupoid , Matui-type groupoid homology is built from the nerve via the Moore complex of compact…