Submission date: 17 October 2020

Abstract:

We give category-theoretic reformulations of stability, NIP, NTP, and non-dividing by observing that their characterisations in terms of indiscernible sequences are naturally expressed as Quillen lifting properties %(negation) of certain morphisms associated with linear orders, in a certain category extending the categories of topological spaces and of simplicial sets.
This suggests an approach to a homotopy theory for model theory.

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Full text: revised version, 12 November 2020: pdf, ps (older version arXiv 2010.08791).