The goal of this paper is to introduce the notions of (L, M)-double fuzzy ideals and (L, M)-double fuzzy ideal bases where L and M are strictly two-sided, commutative quanta and also investigate the relationships between these two structures. Then, we construct a functor from the category of (L, M)-double fuzzy ideal spaces to the category of (L, M)-double fuzzy cotopological spaces. Furthermore, we show the existence of the initial and the final (L, M)-double fuzzy ideal base structures. In particular, we define product of (L, M)-double fuzzy ideal bases.