Fixpoints revisited

  • J. Lambek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 363)


This is an attempt to update some old results by the author on least fixpoints of endofunctors of categories. It is now assumed that the categories in question are cartesian or bicartesian closed and that the functors can be expressed as polynomials. Moreover, in place of completeness one now requires only a weak kind of product in addition to joint equalizers of families of pairs of arrows. Nonetheless, the actual construction of least fixpoints has remained essentially the same. To find examples of categories with these properties a general method is described for adjoining equalizers to categories without sacrificing other structure.


Initial Object Arbitrary Family Admissible Family Polynomial Family Springer LNCS 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. Lambek
    • 1
  1. 1.Mathematics DepartmentMcGill UniversityMontrealCanada

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