Abstract:

 The products and coproducts in the category of L-fuzzy complete lattices are discussed, which consists of L-fuzzy complete lattices and mappings preserving the suprema of arbitrary L-fuzzy sets. The concrete structures of the products and coproducts in this category are given, which generalizes the case of the category of classical complete lattices. The study of products and coproducts lays a foundation on the study of the other properties of the category of L-fuzzy complete lattices.

Key words: L-fuzzy poset; L-fuzzy complete lattice; category; product; coproduct