The Smash Product of Monoidal Theories
The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpreta...
Uloženo v:
| Vydáno v: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 13 |
|---|---|
| Hlavní autor: | |
| Médium: | Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
IEEE
29.06.2021
|
| Témata: | |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpretation (and vast generalisation) of this construction as a low-dimensional projection of a "smash product of pointed directed spaces". Here directed spaces are embodied by combinatorial structures called diagrammatic sets, while Gray products replace cartesian products. The correspondence is mediated by a web of adjunctions relating diagrammatic sets, pros, probs, props, and Gray-categories. The smash product applies to presentations of higher-dimensional theories and systematically produces higher-dimensional coherence data. |
|---|---|
| AbstractList | The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpretation (and vast generalisation) of this construction as a low-dimensional projection of a "smash product of pointed directed spaces". Here directed spaces are embodied by combinatorial structures called diagrammatic sets, while Gray products replace cartesian products. The correspondence is mediated by a web of adjunctions relating diagrammatic sets, pros, probs, props, and Gray-categories. The smash product applies to presentations of higher-dimensional theories and systematically produces higher-dimensional coherence data. |
| Author | Hadzihasanovic, Amar |
| Author_xml | – sequence: 1 givenname: Amar surname: Hadzihasanovic fullname: Hadzihasanovic, Amar email: amar@cs.ioc.ee organization: Tallinn University of Technology,Department of Software Science,Tallinn,Estonia |
| BookMark | eNotj0FLwzAYQCMoqLO_QJCcvLV-35ekSY5SdA4qCpvnkfZLWWVrpJkH_72CO73DgwfvWpxPaYpC3CFUiOAf2lWzNkS1rggIK68tGGvOROGtw7o2Wjtv6ktR5PwJAOQsgvZX4n6zi3J9CHkn3-fE3_1RpkG-pimNHPbyz6Z5jPlGXAxhn2Nx4kJ8PD9tmpeyfVuumse2DOT8seTo2CjjIQy263tHHpxmVgFAKUWdjcjRstN68IzO9AAWNCMROghdpxbi9r87xhi3X_N4CPPP9nSjfgGYb0Ch |
| ContentType | Conference Proceeding |
| DBID | 6IE 6IH CBEJK RIE RIO |
| DOI | 10.1109/LICS52264.2021.9470575 |
| DatabaseName | IEEE Electronic Library (IEL) Conference Proceedings IEEE Proceedings Order Plan (POP) 1998-present by volume IEEE Xplore All Conference Proceedings IEEE Electronic Library (IEL) IEEE Proceedings Order Plans (POP) 1998-present |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISBN | 9781665448956 1665448954 |
| EndPage | 13 |
| ExternalDocumentID | 9470575 |
| Genre | orig-research |
| GroupedDBID | 6IE 6IH ACM ALMA_UNASSIGNED_HOLDINGS APO CBEJK GUFHI LHSKQ RIE RIO |
| ID | FETCH-LOGICAL-a289t-de8d53590af7bcc829084dd3a003332b7e1de7d844f9d185c00704d122180abb3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000947350400031&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| IngestDate | Wed Aug 27 02:23:08 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a289t-de8d53590af7bcc829084dd3a003332b7e1de7d844f9d185c00704d122180abb3 |
| PageCount | 13 |
| ParticipantIDs | ieee_primary_9470575 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-June-29 |
| PublicationDateYYYYMMDD | 2021-06-29 |
| PublicationDate_xml | – month: 06 year: 2021 text: 2021-June-29 day: 29 |
| PublicationDecade | 2020 |
| PublicationTitle | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science |
| PublicationTitleAbbrev | LICS |
| PublicationYear | 2021 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| SSID | ssj0002871049 |
| Score | 2.210637 |
| Snippet | The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories.... |
| SourceID | ieee |
| SourceType | Publisher |
| StartPage | 1 |
| SubjectTerms | Coherence Computer science Tensors |
| Title | The Smash Product of Monoidal Theories |
| URI | https://ieeexplore.ieee.org/document/9470575 |
| WOSCitedRecordID | wos000947350400031&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NSwMxEB3a4sFT1Vb8Jgfx5LZNNtsk52JRKKVQld5KkkmxoN3SD3-_me1aEbx4C8suS76YN5O89wBu4xLyyqJMkGQAZJbaxAnHE0H22jY2VSGl9DpQw6GeTMyoAvd7LkwIobh8FlrULM7yMfdbKpW1jVQEL6pQVaq742rt6ymE_CPaLUnAvGPag6femNAFVU4Eb5Uf_3JRKYJIv_6_3x9B84eNx0b7OHMMlbA4gfq3HQMrd2cD7uKUs_GHXb_R66TjyvIZi5s2n6N9ZwULP-bFTXjpPzz3HpPSBiGxMRvaJBg0ZmlmOnamnPd08qklYmrJhy2Noxk4BoVaypnBGH49SfhI5CJG7451Lj2F2iJfhDNgKDXnNhMuoh4pTdDdoH2GMSlzIg1dPIcGdXu63CldTMseX_z9-BIOaWTp4pQwV1DbrLbhGg7852a-Xt0U0_MFQWGOGA |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NTwIxEJ0gmugJFYzf9mA8uUC7XbY9EwnElZCAhhvpdkokUdbw4e-3s6wYEy_ems1usv3KvJn2vQdw65eQjQ3KAEkGQEahCVKR8kCQvbbxzTiXUnpJ4n5fjcd6UIL7LRfGOZdfPnN1auZn-ZjZNZXKGlrGBC92YDeSPu_ZsLW2FRXC_h7vFjRg3tSNpNceEr6g2ong9eLzXz4qeRjpVP73A4dQ--HjscE20hxByc2PofJtyMCK_VmFOz_pbPhulq_0Oim5smzK_LbNZmjeWM7D95lxDZ47D6N2NyiMEALj86FVgE5hFEa6aaZxai2dfSqJGBpyYgv9eDqOLkYl5VSjD8CWRHwkcuHjd9OkaXgC5Xk2d6fAUCrOTSRSj3uk1E61nLIR-rQsFaFr4RlUqduTj43WxaTo8fnfj29gvzt6SiZJr_94AQc0ynSNSuhLKK8Wa3cFe_ZzNVsurvOp-gLal5Ff |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=Proceedings+of+the+36th+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=The+Smash+Product+of+Monoidal+Theories&rft.au=Hadzihasanovic%2C+Amar&rft.date=2021-06-29&rft.pub=IEEE&rft.spage=1&rft.epage=13&rft_id=info:doi/10.1109%2FLICS52264.2021.9470575&rft.externalDocID=9470575 |