On the Categories of Induced and Weakly Induced <i>LM</i> -G-filter Spaces

In this paper, the authors study the category of [Formula: see text]-G-filter spaces and identify certain subcategories of [Formula: see text]-G-filter spaces. In the process, the concepts of weakly induced [Formula: see text]-G-filter spaces and induced [Formula: see text]-G-filter spaces are introduced. It is proved that [Formula: see text]- FYG, the category of [Formula: see text]-fuzzifying G-filter spaces, is isomorphic to [Formula: see text]- G, the category of induced [Formula: see text]-G-filter spaces. Further, the categorical connection between [Formula: see text]- G, the category of weakly induced [Formula: see text]-G-filter spaces, and [Formula: see text]- G is investigated. It is also proved that [Formula: see text]- G is an isomorphism-closed, bireflective and bicoreflective full subcategory of [Formula: see text]- G.