  A symmetric monoidal category is a category equipped with an associative and
commutative (binary) product and an object which is the unit for the product.
In fact, those properties only hold up to natural isomorphisms which satisfy
some coherence conditions. The coherence theorem asserts the commutativity of
all linear diagrams involving the left and right unitors, the associator and
the braiding.
  We prove the coherence for symmetric monoidal categories using a homotopical
method based on rewriting. For that scope, we detail the con vergence proof of
Lafont's string diagram rewriting system which presents the isomorphisms of
these theories.

Category Theory