A Gray-categorical pasting theorem

The notion of Gray-category, a semi-strict 3-category in which the middle four interchange is weakened to an isomorphism, is central in the study of threedimensional category theory. In this context it is common practice to use 2-dimensional pasting diagrams to express composites of 2-cells, however there is no thorough treatment in the literature justifying this procedure. We fill this gap by providing a formal approach to pasting in Gray-categories and by proving that such composites are uniquely defined up to a contractible groupoid of choices.