## (Co)localisation of one-dimensional model structures

### Richard Garner – 22 November 2017

This is step zero in a project to understand (co)localisation of model categories from a perspective which does not make use of Smith's theorem, but only the constructions of lifting of model structures along right and left adjoint functors.

It is only step zero, because we only fulfil it here for model structures enriched over the model category of 0-types; that is, ones for which the liftings involved in a model structure are unique. Despite being homotopically trivial, it turns out that there are mathematically meaningful examples of such model structures arising in algebraic geometry.

This is joint work with Scott Balchin.

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