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Algebra i Analiz, 2018, Volume 30, Issue 1, Pages 32–95 (Mi aa1571)  
Research Papers

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
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Abstract: 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.
Keywords: 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.
Received: 09.09.2017
English version:
St. Petersburg Mathematical Journal, 2019, Volume 30, Issue 1, Pages 25–71
DOI: https://doi.org/10.1090/spmj/1529
Bibliographic databases:
Document Type: Article
MSC: 06D72
Language: English
Citation: N. V. Durov, “Homotopy theory of normed sets II. Model categories”, Algebra i Analiz, 30:1 (2018), 32–95; St. Petersburg Math. J., 30:1 (2019), 25–71
Citation in format AMSBIB
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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