Coherence, Homotopy and 2-Theories

Noson S. Yanofsky

Coherence, Homotopy and 2-Theories

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arxiv math/0007033 v1 pith:NJ2GIAN7 submitted 2000-07-06 math.CT math.QA

Noson S. Yanofsky This is my paper · ORCID

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keywords theoriesstructurecategorycoherencebiequivalencecategorieshomotopymodel

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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.

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Controlled theories, categorification, and homotopification
math.CT 2026-07 reject novelty 7.0 of 10

Controlled theories yield functorial Lawvere 2-theories and simplicial Lawvere theories, producing a new model of ∞-groups and a candidate for infinite loop spaces.

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