Separation axioms as lifting properties

2017/06/28 by Misha Gavrilovich, Gavrilovich, Misha
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #Constraint Satisfaction and Optimization

paper · pdf · doi:10.48550/arxiv.1706.09164

Abstract

We observe that many of the separation axioms of topology (including T₀-T₄) can be expressed concisely and uniformly in terms of category theory as lifting properties (in the sense of Quillen model categories) with respect to (usually open) continuous maps of finite spaces (involving up to 4 points) and the real line.

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