c0 is not a projective Banach lattice, and c0 is complemented in FBL[c0], implying FBL[c0] is not projective.
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On the Banach lattice c_0
c0 is not a projective Banach lattice, and c0 is complemented in FBL[c0], implying FBL[c0] is not projective.