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Статья «HOMOTOPY THEORY OF NORMED SETS II. MODEL CATEGORIES, "Алгебра и анализ"»

Авторы:
  • DUROV N. V.1
стр. 32-95
Платно
1 St. Petersburg Department of the Steklov Mathematical Institute
  • SDI: 007.001.0234-0852.2018.030.001.3
Ключевые слова:
  • 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
Аннотация:
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.

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