  I motivate a variation (due to K. Szlach\'{a}nyi) of monoidal categories
called skew-monoidal categories where the unital and associativity laws are not
required to be isomorphisms, only natural transformations. Coherence has to be
formulated differently than in the well-known monoidal case. In my (to my
knowledge new) version, it becomes a statement of uniqueness of normalizing
rewrites. I present a proof of this coherence theorem and also formalize it
fully in the dependently typed programming language Agda.
