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http://hdl.handle.net/1942/37131
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DC Field | Value | Language |
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dc.contributor.author | Coulembier, Kevin | - |
dc.contributor.author | Street, Ross | - |
dc.contributor.author | VAN DEN BERGH, Michel | - |
dc.date.accessioned | 2022-03-31T10:15:49Z | - |
dc.date.available | 2022-03-31T10:15:49Z | - |
dc.date.issued | 2021 | - |
dc.date.submitted | 2022-03-25T11:50:11Z | - |
dc.identifier.citation | MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 31 (7) , p. 748 -768 | - |
dc.identifier.uri | http://hdl.handle.net/1942/37131 | - |
dc.description.abstract | Given a monoidal category C with an object J, we construct a monoidal category C [J(v)] by freely adjoining a right dual J(v) to J. We show that the canonical strong monoidal functor Omega : C -> C [J(v)] provides the unit for a biadjunction with the forgetful 2-functor from the 2-category of monoidal categories with a distinguished dual pair to the 2-category of monoidal categories with a distinguished object. We show that Omega : C -> C [J(v)] is fully faithful and provide coend formulas for homs of the form C [J(v)](U, Omega A) and C [J(v)]( Omega A, U) for A is an element of C and U is an element of C [J(v)]. If N denotes the free strict monoidal category on a single generating object 1, then N[1(v)] is the free monoidal category Dpr containing a dual pair - (sic) + of objects. As we have the monoidal pseudopushout C [J(v)] similar or equal to Dpr +(N) C, it is of interest to have an explicit model of Dpr: we provide both geometric and combinatorial models. We show that the (algebraist's) simplicial category Delta is a monoidal full subcategory of Dpr and explain the relationship with the free 2-category Adj containing an adjunction. We describe a generalization of Dpr which includes, for example, a combinatorial model Dseq for the free monoidal category containing a duality sequence X-0 (sic) X-1 (sic) X-2 ... of objects. Actually, Dpr is a monoidal full subcategory of Dseq. | - |
dc.description.sponsorship | The authors gratefully acknowledge the support of Australian Research Council Discovery Grants DE170100623 and DP190102432 | - |
dc.language.iso | en | - |
dc.publisher | CAMBRIDGE UNIV PRESS | - |
dc.rights | The Author(s), 2020. Published by Cambridge University Press | - |
dc.subject.other | Autonomization | - |
dc.subject.other | monoidal dual | - |
dc.subject.other | string diagram | - |
dc.subject.other | adjunction | - |
dc.subject.other | biadjoint | - |
dc.title | Freely adjoining monoidal duals | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 768 | - |
dc.identifier.issue | 7 | - |
dc.identifier.spage | 748 | - |
dc.identifier.volume | 31 | - |
local.format.pages | 21 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Street, R (corresponding author), Macquarie Univ, Dept Math & Stat, Sydney, NSW, Australia. | - |
dc.description.notes | ross.street@mq.edu.au | - |
local.publisher.place | 32 AVENUE OF THE AMERICAS, NEW YORK, NY 10013-2473 USA | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1017/S0960129520000274 | - |
dc.identifier.isi | WOS:000761768700002 | - |
dc.contributor.orcid | Street, Ross/0000-0003-2548-3005 | - |
local.provider.type | wosris | - |
local.description.affiliation | [Coulembier, Kevin] Univ Sydney, Sch Math & Stat, Sydney, NSW, Australia. | - |
local.description.affiliation | [Street, Ross] Macquarie Univ, Dept Math & Stat, Sydney, NSW, Australia. | - |
local.description.affiliation | [van den Bergh, Michel] Hasselt Univ, Dept Math Phys Informat, Diepenbeek, Belgium. | - |
local.uhasselt.international | yes | - |
item.contributor | Coulembier, Kevin | - |
item.contributor | Street, Ross | - |
item.contributor | VAN DEN BERGH, Michel | - |
item.fullcitation | Coulembier, Kevin; Street, Ross & VAN DEN BERGH, Michel (2021) Freely adjoining monoidal duals. In: MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 31 (7) , p. 748 -768. | - |
item.accessRights | Open Access | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2023 | - |
crisitem.journal.issn | 0960-1295 | - |
crisitem.journal.eissn | 1469-8072 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
2004.09697.pdf | Peer-reviewed author version | 304.55 kB | Adobe PDF | View/Open |
EzvDM.pdf Restricted Access | Published version | 291.65 kB | Adobe PDF | View/Open Request a copy |
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