Coherence, Homotopy and 2-Theories

Details Coherence, Homotopy and 2-Theories Coherence, Homotopy and 2-Theories

2000-07-06

arxiv.org/abs/math/0007033v1

Mathematics

Category Theory

32 pages; XY-Pic

Scientific paper

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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