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dc.contributor.authorFemić, Bojanaen_US
dc.contributor.authorGhiorzi, Enricoen_US
dc.date.accessioned2023-02-20T09:39:34Z-
dc.date.available2023-02-20T09:39:34Z-
dc.date.issued2023-
dc.identifier.issn0925-9899-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/5017-
dc.description.abstractWe introduce categories M and S internal in the tricategory Bicat 3 of bicategories, pseudofunctors, pseudonatural transformations and modifications, for matrices and spans in a 1-strict tricategory V. Their horizontal tricategories are the tricategories of matrices and spans in V. Both the internal and the enriched constructions are tricategorifications of the corresponding constructions in 1-categories. Following Fiore et al. (J Pure Appl Algebra 215(6):1174–1197, 2011), we introduce monads and their vertical morphisms in categories internal in tricategories. We prove an equivalent condition for when the internal categories for matrices M and spans S in a 1-strict tricategory V are equivalent, and deduce that in that case their corresponding categories of (strict) monads and vertical monad morphisms are equivalent, too. We prove that the latter categories are isomorphic to those of categories enriched and discretely internal in V, respectively. As a by-product of our tricategorical constructions, we recover some results from Femić (Enrichment and internalization in tricategories, the case of tensor categories and alternative notion to intercategories. arXiv:2101.01460v2). Truncating to 1-categories, we recover results from Cottrell et al. (Tbilisi Math J 10(3):239–254, 2017) and Ehresmann and Ehresmann (Cah Topol Géom Differ Catég 19/4:387–443, 1978) on the equivalence of enriched and discretely internal 1-categories.en_US
dc.publisherSpringer Linken_US
dc.relation.ispartofJournal of Algebraic Combinatoricsen_US
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectBicategory | Double category | Internal and enriched category | Monads | Tricategoryen_US
dc.titleInternalization and enrichment via spans and matrices in a tricategoryen_US
dc.typeArticleen_US
dc.identifier.doi10.1007/s10801-022-01188-1-
dc.identifier.scopus2-s2.0-85145592440-
dc.contributor.affiliationMathematicsen_US
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Artsen_US
dc.description.rank~M22-
item.cerifentitytypePublications-
item.grantfulltextopen-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith Fulltext-
crisitem.author.deptMathematical Institute of the Serbian Academy of Sciences and Arts-
crisitem.author.orcid0000-0002-5767-1708-
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