Coherence for tricategories

This work defines the concept of tricategory as the natural 3-dimensional generalization of bicategory. Trihomomorphism and triequivalence for tricategories are also defined so as to extend the concepts of homomorphism and biequivalence for bicategories. The main theorem is a coherence theorem for tricategories which asserts the existence of a triequivalence between each tricategory and some V-category, where V is the category of 2-categories equipped with the strong tenser product of J. W. Gray. Further, it is shown that while not every tricategory is triequivalent to a 3-category, every tricategory that is locally a 2-category and whose composition is a 2-functor is triequivalent to a 3-category. The work has applications to cohomology theory, homotopy theory, bicategory enriched categories, and bicategories with extra structure.