Fibrations of graphs

In mathematics, a fibration of graphs, or graph fibration, is a homomorphism of directed graphs that satisfies a unique lifting property analogous to that of a fibration in topology.

Intuitively, the target (base) graph is "covered" by the source (total) graph in such a way that each arc of the base can be uniquely lifted to any node in the fibre of its target. The concept (or some of its byproducts) has been independently discovered in several areas, including spectral graph theory, distributed computing, symbolic dynamics, graph neural networks, and category theory, under different names such as graph divisor, left or right covering, left or right-resolving map, equitable partition, color refinement, and Weisfeiler–Leman canonical form.

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