Skip to main content
SpringerLink
Log in

Mealy Morphisms of Enriched Categories

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

We define and study the properties of a notion of morphism of enriched categories, intermediate between strong functor and profunctor. Suggested by bicategorical considerations, it turns out to be a generalization of Mealy machine, well-known since the 1950’s in the theory of computation. When the base category is closed we construct a classifying category for Mealy morphisms, as we call them. This is also seen to give the free tensor completion of an enriched category.

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. Bénabou, J.: Introduction to bicategories. Lect. Notes Math. 47, 1–77 (1967)

    Article  Google Scholar 

  2. Betti, R., Carboni, A., Street, R., Walters, R.F.C.: Variation through enrichment. J. Pure Appl. Algebr. 29, 109–127 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lack, S.: Icons. Appl. Categ. Struct. 18, 289–307 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lawvere, F.W.: Metric spaces, generalized logic and closed categories. Rend. Semin. Mat. Fis. Milano XLIII, 135–166 (1973)

    Article  MathSciNet  Google Scholar 

  5. Lawvere, F.W.: Metric spaces, generalized logic and closed categories. Reprints in Theor. Appl. Categ. 1, 1–37 (2002)

    MathSciNet  Google Scholar 

  6. Linton, F.E.J.: The Multilinear Yoneda Lemmas: Toccata, Fugue and Fantasia on themes by Eilenberg–Kelly and Yoneda. Reports of the midwest category seminar V. Lect. Notes Math. 195, 209–229 (1971)

    Article  MathSciNet  Google Scholar 

  7. Marmolejo, F., Rosebrugh, R., Wood, R.J.: Duality for CCD lattices. Theor. Appl. Categ. 22(1), 1–23 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Mealy, G.: A method for synthesizing sequential circuits. Bell Syst. Tech. J. 34, 1045–1079 (1955)

    MathSciNet  Google Scholar 

  9. Street, R.: Enriched categories and cohomology. Quaest. Math. 6, 265–283 (1983). Reprinted in reprints in Theor. Appl. Categ. 14, 1–18 (2005)

    Article  MathSciNet  Google Scholar 

  10. Walters, R.F.C.: Sheaves and Cauchy-complete categories. Cahiers Topol. Géom. Différ. 22(3), 283–286 (1981)

    MathSciNet  MATH  Google Scholar 

  11. Walters, R.F.C.: Sheaves on sites as Cauchy-complete categories. J. Pure Appl. Algebr. 24, 95–102 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wikipedia: Mealy Machine. http://en.wikipedia.org/wiki/Mealy_machine

  13. Wood, R.J.: Indicial Methods for Relative Categories. Thesis, Dalhousie University (1976)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

    Robert Paré

Authors
  1. Robert Paré
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Paré.

Additional information

Research supported by an NSERC grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paré, R. Mealy Morphisms of Enriched Categories. Appl Categor Struct 20, 251–273 (2012). https://doi.org/10.1007/s10485-010-9238-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-010-9238-8

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation