On category of T-rough sets

Abstract

In this article, we introduce three categories in which their objects are $T$-approximation space and they are denoted by \overline{\textbf{NT}}\textbf{AprS}$, $\overline{\textbf{RNT}}\textbf{AprS}$ and $\overline{\textbf{LNT}}\textbf{AprS}$. We verified the existence or non-existence of products and coproducts in three categories and characterize of epimorphisms and monomorphisms. We discussed equalizer and coequalizer of a pair of morphisms in three categories.