This article tackles categorical coherence within a two-dimensional
generalization of Lawvere's functorial semantics. 2-theories, a syntactical way
of describing categories with structure, are presented. From the perspective
here afforded, many coherence results become simple statements about the
quasi-Yoneda lemma and 2-theory-morphisms. Given two 2-theories and a
2-theory-morphism between them, we explore the induced relationship between the
corresponding 2-categories of algebras. The strength of the induced
quasi-adjoints are classified by the strength of the 2-theory-morphism. These
quasi-adjoints reflect the extent to which one structure can be replaced by
another. A two-dimensional analogue of the Kronecker product is defined and
constructed. This operation allows one to generate new coherence laws from old
ones.Comment: 44 pages, LaTeX; XY-Pic (with 2-cells). Corrected typos and small
change
