Coherence for rewriting 2-theories Export

@article{citeulike:4258899, abstract = {General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language of term rewriting theory. Two general coherence theorems are obtained. The first applies to terminating and confluent rewriting 2-theories. This result is exploited to construct systematic presentations for the higher Thompson groups and the Higman-Thompson groups. The presentations are categorically interesting as they arise from higher-arity analogues of the Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the classical binary axioms. The second general coherence theorem holds for 2-theories that are not necessarily confluent or terminating and is used to construct a new proof of coherence for iterated monoidal categories, which arise as categorical models of iterated loop spaces and fail to be confluent.}, archivePrefix = {arXiv}, author = {Cohen, Jonathan A.}, citeulike-article-id = {4258899}, citeulike-linkout-0 = {http://arxiv.org/abs/0904.0125}, citeulike-linkout-1 = {http://arxiv.org/pdf/0904.0125}, eprint = {0904.0125}, keywords = {category-theory, languages, logic, mathematics, thesis}, month = {Apr}, posted-at = {2009-04-02 17:18:06}, priority = {2}, title = {Coherence for rewriting 2-theories}, url = {http://arxiv.org/abs/0904.0125}, year = {2009} }

TY - JOUR ID - citeulike:4258899 L3 - citeulike-article-id:4258899 N2 - General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language of term rewriting theory. Two general coherence theorems are obtained. The first applies to terminating and confluent rewriting 2-theories. This result is exploited to construct systematic presentations for the higher Thompson groups and the Higman-Thompson groups. The presentations are categorically interesting as they arise from higher-arity analogues of the Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the classical binary axioms. The second general coherence theorem holds for 2-theories that are not necessarily confluent or terminating and is used to construct a new proof of coherence for iterated monoidal categories, which arise as categorical models of iterated loop spaces and fail to be confluent. TI - Coherence for rewriting 2-theories KW - category-theory KW - languages KW - logic KW - mathematics KW - thesis AU - Cohen, Jonathan PY - 2009/Apr/01/ UR - http://arxiv.org/abs/0904.0125 ER -