  This document gives an algebraic and two polygraphic translations of Petri
nets, all three providing an easier way to describe reductions and to identify
some of them. The first one sees places as generators of a commutative monoid
and transitions as rewriting rules on it: this setting is totally equivalent to
Petri nets, but lacks any graphical intuition. The second one considers places
as 1-dimensional cells and transitions as 2-dimensional ones: this translation
recovers a graphical meaning but raises many difficulties since it uses
explicit permutations. Finally, the third translation sees places as
degenerated 2-dimensional cells and transitions as 3-dimensional ones: this is
a setting equivalent to Petri nets, equipped with a graphical interpretation.
