{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/20346"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/20346","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dinatural transformations and polymorphic operators","abstract":"A notion of dinatural transformation more restrictive than that in the literature is presented. Canonical dinatural transformations are defined, and shown to have desirable properties not shared by dinaturals in general. Connections between the notions of canonical dinatural transformation, context-free grammar, initial algebra, and polymorphic operator are elaborated. The theorem that the dinatural transformations between certain functors in the category of partial equivalence relations are exactly the canonical dinaturals is proved. Open questions are discussed, and directions for further study suggested.","abstract_html":"A notion of dinatural transformation more restrictive than that in the literature is presented. Canonical dinatural transformations are defined, and shown to have desirable properties not shared by dinaturals in general. Connections between the notions of canonical dinatural transformation, context-free grammar, initial algebra, and polymorphic operator are elaborated. The theorem that the dinatural transformations between certain functors in the category of partial equivalence relations are exactly the canonical dinaturals is proved. 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Canonical dinatural transformations are defined, and shown to have desirable properties not shared by dinaturals in general. Connections between the notions of canonical dinatural transformation, context-free grammar, initial algebra, and polymorphic operator are elaborated. The theorem that the dinatural transformations between certain functors in the category of partial equivalence relations are exactly the canonical dinaturals is proved. Open questions are discussed, and directions for further study suggested.","Made available in DSpace on 2011-05-07T12:36:36Z (GMT). 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Canonical dinatural transformations are defined, and shown to have desirable properties not shared by dinaturals in general. Connections between the notions of canonical dinatural transformation, context-free grammar, initial algebra, and polymorphic operator are elaborated. The theorem that the dinatural transformations between certain functors in the category of partial equivalence relations are exactly the canonical dinaturals is proved. Open questions are discussed, and directions for further study suggested.","Made available in DSpace on 2011-05-07T12:36:36Z (GMT). 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