Tahere Mohammadi Khorsand - Department of Mathematics, University of Hormozgan, Bandarabbas, Iran
Ghasem Mirhosseinkhani - Department of mathematics and Computer Sciences, Sirjan University of Technology, Sirjan, Iran.

In this paper, we give some generalized categories of topological spaces in terms of monotone operators and investigate some categorical properties of them. In particular, we present some equivalent categories of generalized topological spaces in terms of closure and interior operators. Also, we study the properties of some classes of morphisms as  final, initial, closed and open morphisms in these categories.

Generalized topology, generalized category, monotone operator, closure and interior operator