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

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
Full-text PDF (494 kB)
References:
PDF
HTML
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
\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}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3790744}
\elib{https://elibrary.ru/item.asp?id=32234330}
\transl
\jour St. Petersburg Math. J.
\yr 2019
\vol 30
\issue 1
\pages 25--71
\crossref{https://doi.org/10.1090/spmj/1529}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000452220200003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061791693}
Linking options:
  • https://www.mathnet.ru/eng/aa1571
  • https://www.mathnet.ru/eng/aa/v30/i1/p32
    Cycle of papers
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024