Skip to main content
SpringerLink
Log in

Convexities Generated by L-Monads

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

Let \(\mathbb{F}\) be a monad in the category Comp. We build for each \(\mathbb{F}\)-algebra a convexity in general sense (see van de Vel 1993). We investigate properties of such convexities and apply them to prove that the multiplication map of the order-preserving functional monad is soft.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. van de Vel, M.: Theory of Convex Structures. North-Holland, Amsterdam (1993)

    MATH  Google Scholar 

  2. Eilenberg, S., Moore, J.: Adjoint functors and triples. Ill. J. Math. 9, 381–389 (1965)

    MathSciNet  MATH  Google Scholar 

  3. Radul, T., Zarichnyi, M.: Monads in the category of compacta. Usp. Mat. Nauk 50, 83–106 (1995)

    MathSciNet  Google Scholar 

  4. Teleiko, A., Zarichnyi, M.: Categorical Topology of Compact Hausdorff Spaces. VNTL, Lviv (1999)

  5. Swirszcz, T.: Monadic functors and convexity. Bull. Pol. Acad. Sci. 22, 39–42 (1970)

    MathSciNet  Google Scholar 

  6. de Groot, J.: Supercompactness and superextension. In: Flachsmeyer, J., Poppe, H., Terpe, F. (eds.) Contributions to Extension Theory of Topological Structures. Deutsche Verlag der Wissenschaften, Berlin (1967)

    Google Scholar 

  7. Radul, T.: On functional representations of Lawson monads. Appl. Categ. Struct. 9, 457–463 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. McLane, S.: Categories for Working Mathematicians. Springer, New York (1976)

    Google Scholar 

  9. Radul, T.: On strongly Lawson and I-Lawson monads. Bol. Mat. 6, 69–76 (1999)

    MathSciNet  MATH  Google Scholar 

  10. Radul, T.: On the functor of order-preserving functionals. Comment. Math. Univ. Carol. 39, 609–615 (1998)

    MathSciNet  MATH  Google Scholar 

  11. Zarichnyi, M.: The superextension monad and its algebras. Ukr. Mat. Z. 39, 303–309 (1987)

    MathSciNet  Google Scholar 

  12. Schepin, E.: Functors and uncountable powers of compacta. Usp. Mat. Nauk 36, 3–62 (1981)

    Google Scholar 

  13. Radul, T.: Topology of the space of order-preserving functionals. Bull. Pol. Acad. Sci. Math. 47, 53–60 (1999)

    MathSciNet  MATH  Google Scholar 

  14. Fedorchuk, V., Chigogidze, A.: Absolute retracts and infinitedimensional manifolds, p. 231. Nauka, Moscow (1992)

    Google Scholar 

  15. van Mill, J., van de Vell, M.: Convexity preserving mappings in subbase convexity theory. Proc. Kon. Ned. Acad. Wet. 81, 76–90 (1978)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Lviv National University, Universytetska st., 1, 79000, Lviv, Ukraine

    Taras Radul

Authors
  1. Taras Radul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Taras Radul.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Radul, T. Convexities Generated by L-Monads. Appl Categor Struct 19, 729–739 (2011). https://doi.org/10.1007/s10485-010-9230-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-010-9230-3

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation