Factor Rattans, Category FR(Y), and Factor Space

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The category Fuz can form a WTopos by the use of the middle object and WSC. In this work, we present a new category, category FR(Y), which is based on the idea of factor rattans and factor spaces. The topoi properties of category FR(Y) are investigated. Although FR(Y) is not a topos, it has a middle object and a WSC, and consequently FR(Y) can also form a WTopos. Thus, FR(Y) is another example of a WTopos.