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math.AG2024
Homological smoothness and Deligne resolution for tropical fans
Omid Amini, Matthieu Piquerez
We say that a tropical fan is homologically smooth if each of its open subsets verify tropical Poincare duality. A tropical homology manifold is a tropical variety that is locally…
math.AG2024
Tropical Feichtner-Yuzvinsky and positivity criterion for fans
Omid Amini, Matthieu Piquerez
We prove that the Chow ring of any simplicial fan is isomorphic to the middle degree part of the tropical cohomology ring of its canonical compactification. Using this result, we p…
cs.LO2024
Machine-Checked Categorical Diagrammatic Reasoning
Benoît Guillemet, Assia Mahboubi, Matthieu Piquerez
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This librar…