1999/10/01 by Noson S. Yanofsky, Yanofsky, Noson S.
Mathematics · #18C10 #18D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.CT #math.QA #msc:18C10 #msc:18D10
paper · pdf · doi:10.48550/arxiv.math/9910006
44 pages, LaTeX; XY-Pic (with 2-cells). Corrected typos and small changes
openalex publication_date 1999/10/01 · arxiv created 2000/01/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.