In this paper,the problem of pullback in fuzzy set category L-F is studied.First,the definition of pullback in category L-F is given,and the existence of pullback in category L-F is discussed under the condition that functor f is known to keep the structure of monomorphism or epimorphism on the morphism.Secondly,the definition of slice category is introduced,and it is proved that the slice category L-F/(P,Q)LP of category L-F has pullback when it is known category L-F exists pullback.Finally,the example of special pullback in general category,and the relationship between special pullback and monomorphism is discussed when the category L-F has special pullback is known.
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