dc.contributor.author | Spivak, David I | |
dc.contributor.author | Schultz, Patrick M | |
dc.date.accessioned | 2019-07-09T15:47:01Z | |
dc.date.available | 2019-07-09T15:47:01Z | |
dc.date.issued | 2017 | |
dc.date.submitted | 2016-09 | |
dc.identifier.issn | 0022-4049 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/121541 | |
dc.description.abstract | String 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.sponsorship | United States. Air Force. Office of Scientific Research (grant FA9550–14–1–0031) | en_US |
dc.description.sponsorship | United States. Office of Naval Research ( grant N000141310260) | en_US |
dc.description.sponsorship | United States. National Aeronautics and Space Administration (grant NNH13ZEA001N) | en_US |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.relation.isversionof | https://doi.org/10.1016/j.jpaa.2016.10.009 | en_US |
dc.rights | Creative Commons Attribution-NonCommercial-NoDerivs License | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | en_US |
dc.source | David Spivak | en_US |
dc.title | String diagrams for traced and compact categories are oriented 1-cobordisms | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Spivak, 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.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.approver | David Spivak | en_US |
dc.relation.journal | Journal of Pure and Applied Algebra | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.embargo.terms | N | en_US |
dspace.date.submission | 2019-04-04T10:16:37Z | |
mit.journal.volume | 221 | en_US |
mit.journal.issue | 8 | en_US |
mit.license | PUBLISHER_CC | en_US |