  We construct a finite convergent semi-quadratic presentation for the Chinese
monoid by adding column generators and using combinatorial properties of
insertion algorithms on Chinese staircases. We extend this presentation into a
coherent one whose generators are columns, rewriting rules are defined by
insertion algorithms, and whose syzygies are defined as relations among
insertion algorithms. Such a coherent presentation is used for representations
of Chinese monoids, in particular, it is a way to describe actions of Chinese
monoids on categories.
