Extending to a model structure is not a first-order property

arXiv1410.6127MaRDI QIDQ6255737

Jean-Marie Droz, Inna Zakharevich

Publication date: 22 October 2014

Abstract: Let $mathcalC$ be a finitely bicomplete category and $mathcalW$ a subcategory. We prove that the existence of a model structure on $mathcalC$ with $mathcalW$ as subcategory of weak equivalence is not first order expressible. Along the way we characterize all model structures where $mathcalC$ is a partial order and show that these are determined by the homotopy categories.

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Classical first-order logic (03B10) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Preorders, orders, domains and lattices (viewed as categories) (18B35) Basic properties of first-order languages and structures (03C07)

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