Homotopy theory of normed sets II. Model categories

Durov, N.

doi:10.1090/spmj/1529

Homotopy theory of normed sets II. Model categories
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by N. V. Durov

St. Petersburg Math. J. 30 (2019), 25-71

DOI: https://doi.org/10.1090/spmj/1529

Published electronically: December 5, 2018

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Abstract:

This paper is a continuation of the paper by the same author published in 29 (2017), no. 6 of this journal, where the foundations of the theory of normed and graded sets, and other algebraic structures were laid out. Here these foundations are used to present a homotopy theory of normed and graded sets, and other algebraic structures, by introducing combinatorial model structures on categories of relevant simplicial objects. We also construct a homotopy theory of metric spaces, which turns out to be deeply related to that of normed sets.

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