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In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T 0 reflection. Finally, we introduce some classes of quotient difunctions such as bi-initial and bi-final difunctions between interior-closuredoi:10.2298/fil1505947d fatcat:hk5ncvqyb5ft3js34pwenll7de