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Seminario / Ferreira

Martedi' 23  maggio 2017, alle ore 15.30, in Sala Rappresentanza, 
il Prof. Nelson Martins Ferreira, Instituto Politécnico de Leiria,
terra' un seminario dal titolo:
"A categorical approach to the procedure of transforming a directed graph into a 1-link with applications to additive manufacturing and 3d-printing"
The notion of a link is an abstract structure, which can be defined in an arbitrary category, and it has many applications in additive manufacturing and 3d-printing, namely in modelling all the geometrical, topological, logical and functional information that is involved in the whole process of direct digital manufacturing. One important step, which is used as a key tool in several different stages that occur during the whole process, is the possibility of transforming a directed graph into a 1-link. From a computational point of view this is a simple procedure which is depending on the possibility of sorting the vertices of the directed graph, followed by a consistent sorting of the domain and the codomain maps, and then matching the respective edges. This procedure will create an endomap on the set of edges for the directed graph which, together with the domain map, results in the structure of a 1-link. We will show that there is a deep categorical construction to explain this ad hoc procedure. Moreover, as a consequence, we obtain a (split epimorphism, monomorphism)-factorization system.
This work was supported by the Portuguese Foundation for Science and Technology (FCT) through the Project reference UID/ Multi/04044/2013.
22 maggio 2017
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