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A
model structure for weakly horizontally invariant double
categories
Lyne Moser, Maru Sarazola and Paula Verdugo |
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Algebraic & Geometric Topology 23 (2023) 1725–1786
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Abstract |
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We construct a model structure on the category of double categories and double functors, whose trivial fibrations are the double functors that are surjective on objects, full on horizontal and vertical morphisms, and fully faithful on squares; and whose fibrant objects are the weakly horizontally invariant double categories. We show that the functor , a more homotopical version of the usual horizontal embedding , is right Quillen and homotopically fully faithful when considering Lack’s model structure on . In particular, exhibits a levelwise fibrant replacement of . Moreover, Lack’s model structure on is right-induced along from the model structure for weakly horizontally invariant double categories. We also show that this model structure is monoidal with respect to Böhm’s Gray tensor product. Finally, we prove a Whitehead theorem characterizing the weak equivalences with fibrant source as the double functors which admit a pseudoinverse up to horizontal pseudonatural equivalence. |
Keywords
model structure, double categories, 2–categories, monoidal
model structure, Whitehead theorem
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Mathematical Subject Classification
Primary: 18D20, 18N10, 18N40
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References |
Publication
Received: 27 August 2020
Revised: 16 November 2021
Accepted: 14 December 2021
Published: 14 June 2023
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Authors |
| Lyne Moser | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Maru Sarazola | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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| Paula Verdugo | |
| Department of Mathematics and
Statistics Macquarie University Sydney, NSW Australia |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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