Jing Lu - College of Mathematics and Information Science, Shaanxi Normal Univer- sity, Xi&#۰۳۹;an ۷۱۰۱۱۹, P.R. China
Kaiyun Wang - College of Mathematics and Information Science, Shaanxi Normal University, Xi&#۰۳۹;an ۷۱۰۱۱۹, P.R. China
Bin Zhao - College of Mathematics and Information Science, Shaanxi Normal University, Xi&#۰۳۹;an ۷۱۰۱۱۹, P.R. China

In this paper, we introduce the notion of {\bf K}-flat projective fuzzy quantales, and give an elementary characterization in terms of a fuzzy binary relation on the fuzzy quantale. Moreover, we  prove that {\bf K}-flat projective fuzzy quantales are precisely the coalgebras for a certain comonad on the category of fuzzy quantales. Finally, we present two special cases of {\bf K} as examples.

Fuzzy quantale, Fuzzy binary relation, {bf K}-flat projective fuzzy quantale, Comonad