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Abstract: General coherence theorems are constructed that yield explicit presentationsof categorical and algebraic objects. The categorical structures involved arefinitary discrete Lawvere 2-theories, though they are approached within thelanguage of term rewriting theory. Two general coherence theorems are obtained.The first applies to terminating and confluent rewriting 2-theories. Thisresult is exploited to construct systematic presentations for the higherThompson groups and the Higman-Thompson groups. The presentations arecategorically interesting as they arise from higher-arity analogues of theStasheff-Mac Lane coherence axioms, which involve phenomena not present in theclassical binary axioms. The second general coherence theorem holds for2-theories that are not necessarily confluent or terminating and is used toconstruct a new proof of coherence for iterated monoidal categories, whicharise as categorical models of iterated loop spaces and fail to be confluent.



Author: Jonathan Asher Cohen

Source: https://arxiv.org/







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