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dc.contributor.authorSpivak, David I
dc.contributor.authorSchultz, Patrick M
dc.date.accessioned2019-07-09T15:47:01Z
dc.date.available2019-07-09T15:47:01Z
dc.date.issued2017
dc.date.submitted2016-09
dc.identifier.issn0022-4049
dc.identifier.urihttps://hdl.handle.net/1721.1/121541
dc.description.abstractString diagrams for traced and compact categories are oriented 1-cobordisms David I. Spivak ∗ Patrick Schultz ∗ Massachusetts Institute of Technology, Cambridge, MA 02139 Dylan Rupel † , ‡ Northeastern University, Boston, MA 02115 Abstract We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob / O , where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully en- coded by Cob / O in the sense that there is an equivalence between Cob / O -algebras, for varying O , and traced categories with varying object set. The same holds for compact (closed) categories, the difference being in terms of variance in O . As a consequence of our main theorem, we give a characterization of the 2-category of traced categories solely in terms of those of monoidal and compact categories, without any reference to the usual structures or axioms of traced categories. In an appendix we offer a complete proof of the well-known relationship between the 2-category of monoidal categories with strong monoidal functors and the 2-category of monoidal categories whose object set is free with strict functors; similarly for traced and compact categories.en_US
dc.description.sponsorshipUnited States. Air Force. Office of Scientific Research (grant FA9550–14–1–0031)en_US
dc.description.sponsorshipUnited States. Office of Naval Research ( grant N000141310260)en_US
dc.description.sponsorshipUnited States. National Aeronautics and Space Administration (grant NNH13ZEA001N)en_US
dc.language.isoen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://doi.org/10.1016/j.jpaa.2016.10.009en_US
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivs Licenseen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.sourceDavid Spivaken_US
dc.titleString diagrams for traced and compact categories are oriented 1-cobordismsen_US
dc.typeArticleen_US
dc.identifier.citationSpivak, David I., Patrick Schultz and Dylan Rupel. "String diagrams for traced and compact categories are oriented 1-cobordisms." Journal of Pure and Applied Algebra 221, no. 8 (2017): pp. 2064-2110.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.approverDavid Spivaken_US
dc.relation.journalJournal of Pure and Applied Algebraen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.embargo.termsNen_US
dspace.date.submission2019-04-04T10:16:37Z
mit.journal.volume221en_US
mit.journal.issue8en_US
mit.licensePUBLISHER_CCen_US


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