RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

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.

Full text: PDF file (494 kB)
First page: PDF file
References: PDF file   HTML file

Received: 09.09.2017
Language:

Citation: N. V. Durov, “Homotopy theory of normed sets II. Model categories”, Algebra i Analiz, 30:1 (2018), 32–95

Citation in format AMSBIB
\Bibitem{Dur18}
\by N.~V.~Durov
\paper Homotopy theory of normed sets~II. Model categories
\jour Algebra i Analiz
\yr 2018
\vol 30
\issue 1
\pages 32--95
\mathnet{http://mi.mathnet.ru/aa1571}
\elib{http://elibrary.ru/item.asp?id=32234330}


Linking options:
  • http://mi.mathnet.ru/eng/aa1571
  • http://mi.mathnet.ru/eng/aa/v30/i1/p32

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:153
    References:8
    First page:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019