Skip to main content

Category theoretical methods in topological algebra

  • Conference paper
  • First Online:
Categorical Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 540))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bulman-Fleming S., and H. Werner, Equational compactness in quasi-primal varieties, preprint 1975, 22 pp.

    Google Scholar 

  2. Chen, S., and R. W. Yoh, The category of generalized Lie groups, Trans. Amer. Math. Soc. 199 (1974), 281–294.

    Article  MATH  MathSciNet  Google Scholar 

  3. Choe, T. H., Zero-dimensional compact association distributive universal algebras, Proc. Amer. Math. Soc. 42 (1974), 607–613.

    Article  MATH  MathSciNet  Google Scholar 

  4. Choe, T. H., Injective and projective zero-dimensional compact universal algebras, Alg. Univ. 1976.

    Google Scholar 

  5. Cooper, J. B., Remarks on applications of category theory to functional analysis, preprint 1974, 17 pp.

    Google Scholar 

  6. Cooper, J. B., and P. Michor, Duality of compactological and locally compact groups, preprint 1975, 19 pp.

    Google Scholar 

  7. Dauns, J., Categorical W*-tensor product, Trans. Amer. Math. Soc. 166 (1972), 439–440.

    MATH  MathSciNet  Google Scholar 

  8. Davey, B. A., Duality theory for quasi-varieties of universal algebras, Dissertation, U. Manitoba 1974.

    Google Scholar 

  9. Dieudonné, J., Orientation générale des mathématiques pures en 1973, Gazette des Mathématiciens, Soc. Math. France, Octobre 1974, 73–79.

    Google Scholar 

  10. Eilenberg, S., Sur les groupes compacts d'homéomorphies, Fund. Math. 28 (1937), 75–80.

    MATH  Google Scholar 

  11. Eilenberg, S., and S. MacLane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231–294.

    Article  MATH  MathSciNet  Google Scholar 

  12. Enock, M. and F. M. Schwartz, Une dualité dans les algèbres de von Neumann, C. R. Acad. Sc. Paris 277 (1973), 683–685.

    MATH  MathSciNet  Google Scholar 

  13. Greene, W. A., W* preserves projective limits, Preprint.

    Google Scholar 

  14. Hofmann, K. H., Categories with convergence, exponential functors, and the cohomology of compact abelian groups, Math. Z. 104 (1968) 106–140.

    Article  MATH  MathSciNet  Google Scholar 

  15. Hofmann, K. H., The duality of compact semigroups and C*-bigebras, Lecture Notes in Math. 129, Springer-Verlag, New York, 1970.

    MATH  Google Scholar 

  16. Hofmann, K. H. and K. Keimel, A general character theory for partially ordered sets and lattices, Memoir Amer. Math. Soc. 122, 1972, 121 pp.

    Google Scholar 

  17. Hofmann, K. H. and F. LaMartin, Monoidal categories and monoidal functors, Seminar Notes Tulane University 1971, 103 pp. (limited circulation).

    Google Scholar 

  18. Hofmann, K. H., M. Mislove, and A. Stralka, The Pontryagin Duality of Compact o-Dimensional Semilattices and its Applications, Lecture Notes in Mathematics 396, 1974.

    Google Scholar 

  19. Hofmann, K. H., and P. S. Mostert, Cohomology Theories for Compact Abelian Groups, Dt. Verl. d. Wiss., Berlin and Springer-Verlag, Heidelberg, 1974.

    MATH  Google Scholar 

  20. Hofmann, K. H., and A. Stralka, Mapping cylinders and compact monoids, Math. Ann. 205 (1973), 219–239.

    Article  MATH  MathSciNet  Google Scholar 

  21. Iwasawa, K. On some types of topological groups, Am. Math. 50 (1949), 507–558.

    MATH  MathSciNet  Google Scholar 

  22. Lashof, R. K., Lie algebras of locally compact groups, Pac. J. Math. 7 (1957), 1145–1162.

    Article  MATH  MathSciNet  Google Scholar 

  23. MacLane, S., Categories for the working mathematician, Springer-Verlag, New York, 1971.

    MATH  Google Scholar 

  24. Mitchell, B., Theory of Categories, Academic Press, New York, 1965.

    MATH  Google Scholar 

  25. Numakura, K., Theorems on compact totally disconnected, semigroups and lattices, Proc. Amer. Math. Soc. 8 (1957), 623–626.

    Article  MATH  MathSciNet  Google Scholar 

  26. Pommer, H., Projektive Limites kompakter Räume, Topology 10 (1971), 5–8.

    Article  MATH  MathSciNet  Google Scholar 

  27. Roeder, D. W., Functorial characterizations of Pontryagin duality, Trans. Amer. Math. Soc. 154 (1971), 151–175.

    Article  MATH  MathSciNet  Google Scholar 

  28. Roeder, D. W., Category theory applied to Pontryagin duality, Pac. J. Math. 52 (1974), 519–527.

    Article  MATH  MathSciNet  Google Scholar 

  29. Takesaki, M., Duality and von Neumann algebras, in Lectures on Operator Algebras, Lect. Notes Math. 247, Springer-Verlag, New York 1972, 665–786.

    Book  Google Scholar 

  30. Vainerman, L. I. and G. I. Kac, Nonunimodular ring groups, and Hopf-von Neumann algebras, Dold. Akad. Nauk SSSR 211 (1973), 1031–1034; Soviet Math. Doklady 14 (1973), 1144–1148.

    MathSciNet  Google Scholar 

  31. Wallace, D., Permutation groupoids, Dissertation Tulane University, 1976.

    Google Scholar 

Download references

Authors

Editor information

Ernst Binz Horst Herrlich

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Hofmann, K.H. (1976). Category theoretical methods in topological algebra. In: Binz, E., Herrlich, H. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080866

Download citation

  • DOI: https://doi.org/10.1007/BFb0080866

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07859-3

  • Online ISBN: 978-3-540-38118-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics