Uniform Functors on Sets

  • Lawrence S. Moss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4060)


This paper studies uniformity conditions for endofunctors on sets following Aczel [1], Turi [21], and others. The “usual” functors on sets are uniform in our sense, and assuming the Anti-Foundation Axiom AFA, a uniform functor H has the property that its greatest fixed point H * is a final coalgebra whose structure is the identity map. We propose a notion of uniformity whose definition involves notions from recent work in coalgebraic recursion theory: completely iterative monads and completely iterative algebras (cias). Among our new results is one which states that for a uniform H, the entire set-theoretic universe V is a cia: the structure is the inclusion of HV into the universe V itself.


Natural Transformation Foundation Axiom Equation Morphism Standard Functor Constant Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lawrence S. Moss
    • 1
  1. 1.Mathematics DepartmentIndiana UniversityBloomingtonUSA

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