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Coherence, Homotopy and 2-Theories

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

Coherence, Homotopy and 2-Theories

Noson S. Yanofsky This is my paper
classification math.CT math.QA
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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Cited by 2 Pith papers

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    math.CT 2026-07 conditional novelty 7.0

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

  2. Controlled theories, categorification, and homotopification

    math.CT 2026-07 reject novelty 7.0

    Controlled theories are claimed to yield functorial categorifications and homotopifications, but the central 'strong augmentation' theorem is false for the paper's main examples and Proposition 6.18 asserts Ωmon(n,1) ...