{"id":{"repo_id":"glasgow","oai_identifier":"oai:theses.gla.ac.uk:689"},"canonical_url":"https://search.dev.ndltd.org/etd/glasgow/oai:theses.gla.ac.uk:689","repository":{"repo_id":"glasgow","name":"University of Glasgow","base_url":"https://theses.gla.ac.uk/cgi/oai2"},"display":{"title":"Coherence for categorified operadic theories","abstract":"Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which equations that hold strictly for P -algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and show that the “strictification” functor has an interesting universal property, being left adjoint to the forgetful functor from the category of strict P -categories to the category of weak P -categories. We further show that the categorification obtained is independent of our choice of presentation for P , and extend some of our results to many-sorted theories, using multicategories.","abstract_html":"Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which equations that hold strictly for P -algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and show that the “strictification” functor has an interesting universal property, being left adjoint to the forgetful functor from the category of strict P -categories to the category of weak P -categories. We further show that the categorification obtained is independent of our choice of presentation for P , and extend some of our results to many-sorted theories, using multicategories.","abstract_has_math":false,"creators":["Gould, Miles Richard"],"institution":"University of Glasgow","degree_name":null,"degree_level":"PhD","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-24T02:23:30Z","subjects":["QA Mathematics"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Gould, Miles Richard"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2008"]},{"key":"dc:date.issued","label":"Date","values":["2008"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Glasgow"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://theses.gla.ac.uk/689/"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://gla.on.worldcat.org/oclc/319493720"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://theses.gla.ac.uk/689/1/2009gouldphd.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which equations that hold strictly for P -algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and show that the “strictification” functor has an interesting universal property, being left adjoint to the forgetful functor from the category of strict P -categories to the category of weak P -categories. We further show that the categorification obtained is independent of our choice of presentation for P , and extend some of our results to many-sorted theories, using multicategories."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Coherence for categorified operadic theories"]}]}],"canonical_facts":{"dc:creator":["Gould, Miles Richard"],"dc:date":["2008"],"dc:date.issued":["2008"],"dc:description.abstract":["Given an algebraic theory which can be described by a (possibly symmetric) operad P, we propose a definition of the weakening (or categorification) of the theory, in which equations that hold strictly for P -algebras hold only up to coherent isomorphism. This generalizes the theories of monoidal categories and symmetric monoidal categories, and several related notions defined in the literature. Using this definition, we generalize the result that every monoidal category is monoidally equivalent to a strict monoidal category, and show that the “strictification” functor has an interesting universal property, being left adjoint to the forgetful functor from the category of strict P -categories to the category of weak P -categories. We further show that the categorification obtained is independent of our choice of presentation for P , and extend some of our results to many-sorted theories, using multicategories."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://theses.gla.ac.uk/689/1/2009gouldphd.pdf"],"dc:language":["en"],"dc:publisher.institution":["University of Glasgow"],"dc:relation.isreferencedby":["https://theses.gla.ac.uk/689/"],"dc:relation.isreferencedby.uri":["https://gla.on.worldcat.org/oclc/319493720"],"dc:subject":["QA Mathematics"],"dc:title":["Coherence for categorified operadic theories"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["PhD"]},"updated_at":"2026-07-24T02:23:30Z"}