Applied Categorical Structures

, Volume 27, Issue 1, pp 1–21 | Cite as

Bousfield Localisation and Colocalisation of One-Dimensional Model Structures

  • Scott Balchin
  • Richard GarnerEmail author


We give an account of Bousfield localisation and colocalisation for one-dimensional model categories—ones enriched over the model category of 0-types. A distinguishing feature of our treatment is that it builds localisations and colocalisations using only the constructions of projective and injective transfer of model structures along right and left adjoint functors, and without any reference to Smith’s theorem.


Quillen model structures Bousfield (co)localisation 

Mathematics Subject Classification

Primary 55U35 18A40 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of SheffieldSheffieldUK
  2. 2.Centre of Australian Category Theory, Department of MathematicsMacquarie UniversitySydneyAustralia

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