Categorical properties of M-indiscernibility spaces

This paper discusses categorical aspect of the Pawlak rough set theory. It is proved that the category of all M-indiscernibility spaces and M-equivalence relation-preserving mappings between them is both a topological construct and a topos. As an application of these results, the notions of product M-indiscernibility space, sum M-indiscernibility space, quotient M-indiscernibility space, M-indiscernibility subspace, quotient mapping, and isomorphism mapping are defined, and structures of these M-indiscernibility spaces and mappings are also given.