dc.contributor.author | Haugseng, Rune | |
dc.contributor.author | Hebestreit, Fabian | |
dc.contributor.author | Linskens, Sil | |
dc.contributor.author | Nuiten, Joost | |
dc.date.accessioned | 2024-02-28T14:56:46Z | |
dc.date.available | 2024-02-28T14:56:46Z | |
dc.date.created | 2024-01-02T12:51:56Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Forum of Mathematics, Sigma. 2023, 11, e1111 | en_US |
dc.identifier.issn | 2050-5094 | |
dc.identifier.uri | https://hdl.handle.net/11250/3120352 | |
dc.description.abstract | We prove a universal property for ∞-categories of spans in the generality of Barwick’s adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a self-equivalence on the class of orthogonal adequate triples, which we introduce for this purpose.
As applications of the machinery we develop, we give a quick proof of Barwick’s unfurling theorem, show that an orthogonal factorisation system arises from a cartesian fibration if and only if it forms an adequate triple (generalising work of Lanari), extend the description of dual (co)cartesian fibrations by Barwick, Glasman and Nardin to two-variable fibrations, explicitly describe parametrised adjoints (extending work of Torii), identify the orthofibration classifying the mapping category functor of an (∞,2)-category (building on work of Abellán García and Stern), formally identify the unstraightenings of the identity functor on the ∞-category of ∞-categories with the (op)lax under-categories of a point, and deduce a certain naturality property of the Yoneda embedding (answering a question of Clausen). | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Cambridge University Press | en_US |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no | * |
dc.title | Two-variable fibrations, factorisation systems and -categories of spans | en_US |
dc.title.alternative | Two-variable fibrations, factorisation systems and -categories of spans | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.volume | 11 | en_US |
dc.source.journal | Forum of Mathematics, Sigma | en_US |
dc.identifier.doi | 10.1017/fms.2023.107 | |
dc.identifier.cristin | 2218911 | |
dc.source.articlenumber | e1111 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |