Topos theory plays an important role in modern mathematics. It can be viewed as a generalization of set from the category aspect. However, the category of all fuzzy sets do not form topos. In order to investigate the category properties about fuzzy sets, the notion of weak topos is introduced. Factor space is an effective approach in knowledge representation and factor rattan is a crucial concept of a factor space. Rattans over Y could be viewed as an abstraction of factor rattan. In addition, the category of rattans over Y is not a topos. In this paper, two comments about the paper titled “Factor rattans, category FR(Y), and factor space” (J MATH ANAL APPL, 1994) are presented, and the notion of rattan over Y is revised to complete rattan over Y. The corresponding category is denoted CFR(Y). Topoi properties of the functor category CFR (Y)^C are investigated and it is proved that CFR (Y)^C is a weak topos, but not a topos.