Skip to main content

Cohomology of small categories in homotopical algebra

Part of the Lecture Notes in Mathematics book series (LNM,volume 1437)

Keywords

  • Abelian Group
  • Exact Sequence
  • Natural System
  • Homotopy Class
  • Linear Extension

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baues, H.J.: Algebraic homotopy, appears in Cambridge University Press.

    Google Scholar 

  2. Baues, H.J.: The homotopy types of 4-dimensional CW-complexes, Preprint. MPI. Bonn. 1986.

    Google Scholar 

  3. Baues, H.J. and Wirsching, G.: The cohomology of small categories, J. Pure and Appl. Alg. 38, 1985, 187–211.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Bousfield, A.K. and Kan, D.M.: Homotopy limits, Completions and localization, Lect. Notes Math. 304, 1972.

    Google Scholar 

  5. Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton University Press, 1956.

    Google Scholar 

  6. Curtis, E.B.: Some relations between homotopy and homology. Ann. of Math. 83, 1965, 386–413.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Datuashvili, T.: On cohomology of small categories. Proc. Mat. Institut Tbilisi, 62, 1979, 28–37. /Russian/.

    MathSciNet  MATH  Google Scholar 

  8. Dold, A. and Puppe, D.: Homologie nicht-additivez Functoren. Anwendungen, Ann. Inst. Fourier, 11, 1961, 201–312.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Holt, O.F.: An interpretation of the cohomology groups Hn(G,M). J. Algebra, 60, 1979, 307–318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Huebschmann, J.: Crossed n-fold extensions of groups and cohomolgy. Comm. math. Helv. 55, 1980, 302–314.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Inasaridze, H.: Some aspects of homological and homotopical algebra and its applications. Proc. math. inst. Tbilisi 48, 1975, 1–140. /Russian/.

    MathSciNet  Google Scholar 

  12. Jibladze, M. and Pirashvili, T.: On some linear extension of the category of finitely generated free modules. Bull. Ac. Sc. Georgian SSR, 123, 3, 1986, 481–484. /Russian/.

    MathSciNet  MATH  Google Scholar 

  13. Jibladze, M. and Pirashvili, T.: Cohomology of algebraic theories /to appear/.

    Google Scholar 

  14. Loday, J.L.: Cohomologie et groupe de Steinberg relatifs. J. Algebra, 54, 1978, 178–202.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Loday, J.L.: Spaces with finitely many nontrivial homotopy groups. J. Pure and Appl. Algebra, 24, 1982, 179–202.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. May, J.P.: Simplicial objects in Algebraic Topology. Princeton: Van Nostrand, 1967.

    MATH  Google Scholar 

  17. Pirashvili, T.: Cohomology of small categories and models for homotopy theories. Bull. Ac. Sc. Georgian SSR, 129, 2, 1988, 261–264 /Russian/.

    MathSciNet  MATH  Google Scholar 

  18. Quillen, D.: Homotopical algebra. Lect. Notes Math. 43, 1967.

    Google Scholar 

  19. Quillen, D.: Higher algebraic K-theory I, Lect. Notes Math. 341, 1973, 85–147.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Schubert, H.: Kategorien. Bd. II. Springer. Berlin. 1970.

    CrossRef  MATH  Google Scholar 

  21. Unsöld, H.M.: On classification of spaces with free homology. Freien Universität Berlin, 1987.

    Google Scholar 

  22. Witt,E.: Treue Darstellung Liescher Ring. J. reine und angew. Math. 177, 152–160.

    Google Scholar 

  23. Whitehead, J.H.C.: Certain exact sequence. Ann. Math. 52, 1950, 51–110.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. Yoneda, N.: On Ext and Exact sequences. J.Fac.Sci.Tokyo.Sec.I. 1960, V.8, 507–526.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Pirashvili, T. (1990). Cohomology of small categories in homotopical algebra. In: Inassaridze, H. (eds) K-theory and Homological Algebra. Lecture Notes in Mathematics, vol 1437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086724

Download citation

  • DOI: https://doi.org/10.1007/BFb0086724

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52836-4

  • Online ISBN: 978-3-540-47162-2

  • eBook Packages: Springer Book Archive