Homotopy theory of normed sets II. Model categories
N. V. Durov
St. Petersburg Department of the Steklov Mathematical Institute, 27 Fontanka emb., 191023, St. Petersburg, Russia
This paper is a continuation of the paper by the same author published in no. 2017:6 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.
normed sets, normed groups, norms, normed algebraic structures, graded algebraic structures, filtered algebraic structures, fuzzy sets, linear logic, presheaf categories, finitary monads, generalized rings, metric spaces, model categories, homotopy categories, higher categories.
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N. V. Durov, “Homotopy theory of normed sets II. Model categories”, Algebra i Analiz, 30:1 (2018), 32–95
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\paper Homotopy theory of normed sets~II. Model categories
\jour Algebra i Analiz
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