by
Noson S. Yanofsky

@MISC{Yanofsky99thesyntax,

author = {Noson S. Yanofsky},

title = {The Syntax of Coherence},

year = {1999}

}

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-theorymorphism. 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. 1

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