Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories
Category Theory
2026-05-01 v1 General Topology
Abstract
We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also show that, by means of this isomorphism, the topology associated with a quasi-pseudometric modular coincides with that generated by its corresponding quantale enriched category. Furthermore, we demonstrate that the class of quasi-pseudometrizable topological spaces coincides with the topological spaces whose topology is induced by a quasi-pseudometric modular.
Cite
@article{arxiv.2604.27588,
title = {Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories},
author = {César López-Pastor and Tatiana Pedraza and Jesús Rodríguez-López},
journal= {arXiv preprint arXiv:2604.27588},
year = {2026}
}
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20 pages