  In a paper by Ford, it is claimed that to any pushout square of categories
with all involved functors injective, there is associated an exact
"Mayer--Vietoris" sequence of derived (co)limits. We provide a counter-example
to this general statement. Further, we construct the Mayer--Vietoris sequence
under some restrictions that cover the well-known case of a pushout square of
group monomorphisms.
