Jonathan Scott (Cleveland State University)
Abstract: A weighted category is one in which each arrow has a `cost' associated to it. In this talk, we will define a Gromov-Hausdorff distance between weighted categories. We use the resulting framework to generalize the interleaving distance of persistence modules. The key ingredient is the bicategory of ``pairwise embeddings'', a certain sub-bicategory of cospans. This is joint work with Peter Bubenik and Vin de Silva.
Generalized Gromov-Hausdorff Distance and Interleavings of Functors