Technical report, 2002.

[*Note: This paper essentially uses the resolution condition of MALL
proof nets to characterise the free product-sum category. It was
never published as it turned out Hongde Hu had already
characterised the free category: Contractible coherence
spaces and maximal maps, ENTCS 20, 1999. The proof in
the technical report can be shortened considerably because of this
prior art.*]

Cockett and Seely recently introduced a Lambek-style deductive system
for finite products and sums, and proved decidability of equality of
morphisms. The question remained as to whether one can present free
categories with finite products and sums in a canonical way,
*i.e.*, as a category with morphisms and composition defined
directly, rather than modulo equivalence relations. This paper shows
that the non-empty case (*i.e.*, omitting initial and final
objects) can be treated in a surprisingly simple way: morphisms of the
free category can be viewed as certain binary relations, with
composition the usual composition of binary relations. In particular,
there is a forgetful functor into the category
**Rel** of sets and binary relations. The paper ends by relating
these binary relations to proof nets.