Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 8 - Well-Founded Coalgebras

  • Jiří Adámek, Czech Technical University in Prague, Stefan Milius, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, Lawrence S. Moss, Indiana University, Bloomington
  • Book:
    Initial Algebras and Terminal Coalgebras
    Published online:
    30 January 2025
    Print publication:
    06 February 2025, pp 253-292

  • Summary

    Well-founded coalgebras generalize well-foundedness for graphs, and they capture the induction principle for well-founded orders on an abstract level. Taylor’s General Recursion Theorem shows that, under hypotheses, every well-founded coalgebra is parametrically recursive. We give a new proof of this result, and we show that it holds for all set functors, and for all endofunctors preserving monomorphisms on a complete and well-powered category with smooth monomorphisms. The converse of the theorem holds for set functors preserving inverse images. We provide an iterative construction of the well-founded part of a given coalgebra: It is carried by the least fixed point of Jacobs’ next-time operator.