  If $X$ is a quasi-compact and quasi-separated scheme, the category $Qcoh(X)$
of quasi-coherent sheaves on $X$ is locally finitely presented. Therefore
categorical flat quasi-coherent sheaves naturally arise. But there is also the
standard definition of flatness in $Qcoh(X)$ from the stalks. So it makes sense
to wonder the relationship (if any) between these two notions. In this paper we
show that there are plenty of locally finitely presented categories having no
other categorical flats than the zero object. As particular instance, we show
that $Qcoh(\mathbf{P}^n(R)))$ has no other categorical flat objects than zero,
where $R$ is any commutative ring.
