  The generality of a derivation is an equivalence relation on the set of
occurrences of variables in its premises and conclusion such that two
occurrences of the same variable are in this relation iff they must remain
occurrences of the same variable in every generalization of the derivation. The
variables in question are propositional or of another type. This paper examines
in the setting of categorial proof theory the conjecture that two derivations
with the same premises and conclusions stand for the same proof iff they have
the same generality. For that purpose generality is defined within a category
whose arrows are equivalence relations on finite ordinals, where composition is
rather complicated. Several examples are given of deductive systems of
derivations covering fragments of logic, with the associated map into the
category of equivalence relations of generality. This category is
isomorphically represented in the category whose arrows are binary relations
between finite ordinals, where composition is the usual simple composition of
relations. This representation is related to a classical representation result
of Richard Brauer.
