  The construction of a category of spans can be made in some categories $\CC$
which do not have pullbacks in the traditional sense. The PROP for monoids is a
good example of such a $\CC$. The 2012 book concerning homological algebra by
Marco Grandis gives the proof of associativity of relations in a Puppe-exact
category based on a 1967 paper of M.\v{S}. Calenko. The proof here is a
restructuring of that proof in the spirit of the first sentence of this
Abstract. We observe that these relations are spans of EM-spans and that
EM-spans admit fake pullbacks so that spans of EM-spans compose. Our setting is
more general than Puppe-exact categories.
