The following preprint is available on the xxx.lanl.gov archive: http://xxx.lanl.gov/abs/math.CT/0007033 Coherence, Homotopy and 2-Theories Authors: Noson S. Yanofsky Comments: 32 pages; XY-Pic Subj-class: Category Theory; Quantum Algebra MSC-class: 18D10; 18C10; 55U35 2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a Quillen model category structure on the category of 2-theories and 2-theory-morphisms where the weak equivalences are biequivalences of 2-theories. A biequivalence of 2-theories (Morita equivalence) induces and is induced by a biequivalence of 2-categories of algebras. This model category structure allows one to talk of the homotopy of 2-theories and discuss the universal properties of coherence. All the best, Noson