UCLouvain-ULB-VUB Category Theory Seminar

by Prof. Luca Spada (Università degli Studi di Salerno))

Monday 15 Jun 2026, 16:30 → 18:30 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

Luca Spada (Università degli Studi di Salerno) :  Some categorical properties of (rational) polyhedra

MV-algebras, the algebraic semantics of Lukasiewicz logic, have a nice connection with combinatorial geometry. The category of finitely presented MV-algebras is duality equivalent to the category of polyhedra with rational vertices and Z-maps between them. In this talk, I will show that the latter category is coherent and extensive. Z-maps are defined as continuous piecewise affinely linear maps in which every linear piece has integer coefficients. The combinatorial aspects of piecewise linearity intertwine with the arithmetic constraints of integer coefficients; to prove our result, we provide a categorical description of (rational) polyhedra that allows us to detangle these two aspects. This description is also connected with the notion of definable sets in o-minimal structures.
This is joint work with Matias Menni.