Seminár z teórie grafov - Gejza Jenča (24.4.2025)
vo štvrtok 24.4.2025 o 9:50 hod. v miestnosti M 213
Prednášajúci: Gejza Jenča (Slovenská technická univerzita, Bratislava)
Názov: Voltage Lifts of Graphs from a Category Theory Viewpoint
Termín: 24.4.2025, 9:50 hod., M 213
Abstrakt:
A voltage graph is a graph (symmetric multidigraph) in which every dart is labeled with an element of a group in a way that respects the involutive symmetry. A group labelled graph is a graph in which every vertex is labelled by a element of a group.
In 1974, Gross introduced a construction of a derived graph of a voltage graph. Nowadays, this construction is called voltage graph lift.
In the talk, we give a category theoretical background of this construction by showing that the voltage graph lift is a functor that is right adjoint to a (very naturally defined) functor from the category of group labelled graphs to the category of voltage graphs.
We then show that it is possible to describe the lift construction as a pullback in the category of graphs. This allows us to consider a wider category of voltage graphs, for which the underlying group in not fixed.