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In this article we extend the theory of lax monoidal structures, also knownas multitensors, and the monads on categories of enriched graphs that they giverise to. Our first principal result -- the lifting theorem for multitensors --enables us to see the Gray tensor product of 2-categories and the Crans tensorproduct of Gray categories as part of this framework. We define weakn-categories with strict units by means of a notion of reduced higher operad,using the theory of algebraic weak factorisation systems. Our second principalresult is to establish a lax tensor product on the category of weakn-categories with strict units, so that enriched categories with respect tothis tensor product are exactly weak (n+1)-categories with strict units.

Multitensor lifting and strictly unital higher category theory