Princess Blaze the Cat isn't from Mobius, rather a almost-identical dimension called Solbius, Blaze in particular was born on the Sol Empire, the Acorn Archipelago equivalent of the Sol Dimension. Blaze's family carries the task of protecting the Sol Emeralds, these gemstones share the same history as the Chaos Emeralds, except that they give elemental powers instead of more generic super powers. After a event involving the Master Emerald and the Jeweled Scepter (the Sol Dimension equivalent of the Master Emerald), Blaze was able to visit the other dimension, and make friends with some of its inhabitants. And despite her duties and strict mother, she does wish to one day return to the other dimension.