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dc.contributor.authorDošen, Kostaen
dc.contributor.authorPetrić, Zoranen
dc.date.accessioned2020-04-12T18:10:33Z-
dc.date.available2020-04-12T18:10:33Z-
dc.date.issued2012-02-01en
dc.identifier.issn0927-2852en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/331-
dc.description.abstractThis paper proves coherence results for categories with a natural transformation called intermutation made of arrows from (A ∨ B) ∧ (C ∨ D) to (A ∨ C) ∧ (B ∨ D), for ∧ and ∨ being two biendofunctors. Intermutation occurs in iterated, or n-fold, monoidal categories, which were introduced in connection with n-fold loop spaces, and for which a related, but different, coherence result was obtained previously by Balteanu, Fiedorowicz, Schwanzl and Vogt. The results of the present paper strengthen up to a point this previous result, and show that twofold loop spaces arise in the manner envisaged by these authors out of categories of a more general kind, which are not two-fold monoidal in their sense. In particular, some categories with finite products and coproducts are such. Coherence in Mac Lane's "all diagrams commute" sense is proved here first for categories where for ∧ and ∨ one assumes only intermutation, and next for categories where one also assumes natural associativity isomorphisms. Coherence in the sense of coherence for symmetric monoidal categories is proved when one assumes moreover natural commutativity isomorphisms for ∧ and ∨. A restricted coherence result, involving a proviso of the kind found in coherence for symmetric monoidal closed categories, is proved in the presence of two nonisomorphic unit objects. The coherence conditions for intermutation and for the unit objects are derived from a unifying principle, which roughly speaking is about preservation of structures involving one endofunctor by another endofunctor, up to a natural transformation that is not an isomorphism. This is related to weakening the notion ofmonoidal functor.Asimilar, but less symmetric, justification for intermutation was envisaged in connection with iterated monoidal categories. Unlike the assumptions previously introduced for two-fold monoidal categories, the assumptions for the unit objects of the categories of this paper, which are more general, allow an interpretation in logic.en
dc.publisherSpringer Link-
dc.relationMinistry of Science of Serbia (Grants 144013 and 144029)-
dc.relation.ispartofApplied Categorical Structuresen
dc.subjectAssociativity | Coherence | Commutativity | Iterated monoidal categories | Loop spaces | Monoidal categories | Symmetric monoidal categoriesen
dc.titleIntermutationen
dc.typeArticleen
dc.identifier.doi10.1007/s10485-010-9228-xen
dc.identifier.scopus2-s2.0-84863503946en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage43en
dc.relation.lastpage95en
dc.relation.issue1en
dc.relation.volume20en
dc.description.rankM23-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
item.grantfulltextnone-
item.openairetypeArticle-
item.cerifentitytypePublications-
crisitem.author.orcid0000-0003-2049-9892-
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