Skip to main content
Log in

Homotopy inverses for nerve

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  1. Barratt, M.G.: Simplicial and semi-simplicial complexes. Seminar notes, Princeton 1956

  2. Brown, R.: Elements of Modern Topology. London: MacGraw-Hill 1968

    Google Scholar 

  3. Cartan, H., Eilenberg, S.: Homological Algebra. Princeton, New Jersey: Princeton University Press, 1956

    Google Scholar 

  4. Fritsch, R.: On subdivision of semisimplicial sets. Proceedings of the International Symposium on Topology and its Applications. Herceg-Novi, 1968, 25–31. 8., 156–163

  5. Fritsch, R.: Zur Unterteilung semisimplizialer Mengen. I. Math. Z.108, 329–367 (1969), II. Math. Z.109, 131–152 (1969)

    Google Scholar 

  6. Fritsch, R.: Some remarks on S. Weingram: On the triangulation of a semisimplicial complex [8], Illinois J. of Math.14, 529–535 (1970)

    Google Scholar 

  7. Fritsch, R.: Charakterisierung semisimplizialer Mengen durch Unterteilung und Graphen. Manuscripta Math.5, 213–227 (1971)

    Google Scholar 

  8. Fritsch, R.: Simpliziale und semisimplizale Mengen. Bull. de l'Acad. Polonaise des Sci.,20, 159–169 (1972)

    Google Scholar 

  9. Fritsch, R., Latch, D.M.: Homotopy inverses for nerve. Bull. of Amer. Math. Soc. (New Series)1, 258–262 (1979)

    Google Scholar 

  10. Gabriel, R., Zisman, M.: Calculus of Fractions and Homotopy Theory. Berlin and New York: Springer 1967

    Google Scholar 

  11. Illusie, L.: Complex Cotangent et Deformations II. Lecture Notes in Mathematics, 283, Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  12. Kan, D.M.: Abstract homotopy II. Proc. Nat. Acad. Sci. U.S.A.,42, 255–258 (1956)

    Google Scholar 

  13. Kan, D.M.: On c.s.s. complexes. Amer. J. Math.79, 449–476 (1957)

    Google Scholar 

  14. Kan, D.M.: Functors involving c.c.s. complexes. Trans. Amer. Math. Soc.,87, 330–346 (1958)

    Google Scholar 

  15. Kimura, N.: On Semigroups. Doctoral Dissertation, the Tulane University of Louisiana, 1957

  16. Lamotke, K.: Semisimpliziale algebraische Topologie. Berlin-Heidelberg-New York Springer 1968

    Google Scholar 

  17. Latch, D.M.: The uniqueness of homology for the category of small categories. J. Pure Appl. Algebra,9, 221–237 (1977)

    Google Scholar 

  18. Latch, D.M.: A fibred homotopy equivalence and homology theories for the category of small categories. J. Pure Appl. Algebra,15, 247–269 (1979)

    Google Scholar 

  19. Latch, D.M., Thomason, R.W., Wilson, W.S.: Simplicial sets from categories. Math. Z.164, 195–214 (1979)

    Google Scholar 

  20. Lee, M.J.: Homotopy for functors. Proc. Amer. Math. Soc.,36, 571–577 (1972);42, 648–650 (1974)

    Google Scholar 

  21. Lundell, A.T., Weingram, S.: The Topology of CW complexes. New York: Van Nostrand, 1969

    Google Scholar 

  22. MacLane, S.: Categories for the Working Mathematician. New York: Springer 1971

    Google Scholar 

  23. MacLane, S.: Homology. Berlin-Göttingen-Heidelberg: Springer 1963

    Google Scholar 

  24. Milnor, J.: The geometric realization of a semi-simplicial complex. Ann. of Math. (2)65, 357–362 (1957)

    Google Scholar 

  25. Puppe, D.: Homotopie and Homologie in abelschen Gruppen und Monoidkomplexen. I. Math. Z.68, 367–406 (1958)

    Google Scholar 

  26. Rourke, C.P., Sanderson, B.J.: Δ-Sets I: Homotopy theory. Quart. J. Math. Oxford (2)22, 321–338 (1971)

    Google Scholar 

  27. Ruiz Salguero, C., Ruiz Salguero, R.: Remarks about the Eilenberg-Zilber type decomposition in cosimplicial sets. Revista Colombiana de Mathematicas12, 61–82 (1978)

    Google Scholar 

  28. Segal, G.: Categories and cohomology theories. Topology13, 293–312 (1974)

    Google Scholar 

  29. Segal, J.: Isomorphic complexes. Bull. Amer. Math. Soc.71, 571–572 (1965)

    Google Scholar 

  30. Thomason, R.W.: Cat as a closed model category. Cahiers Topologie Géom. Différentielle21, 305–324 (1980)

    Google Scholar 

  31. Whitehead, J.H.C.: Combinatorial homotopy. I. Trans. Amer. Math. Soc.,55, 213–215 (1949)

    Google Scholar 

  32. Whitehead, J.H.C.: On the asphericity of regions in a 3-sphere. Fund. Math.32, 149–166 (1939)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fritsch, R., Latch, D.M. Homotopy inverses for nerve. Math Z 177, 147–179 (1981). https://doi.org/10.1007/BF01214196

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01214196

Navigation