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1 results

  • 7 - Terminal Coalgebras as Algebras, Initial Algebras as 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 215-252

  • Summary

    Corecursive algebras are algebras that admit unique solutions of recursive equation systems. We study these and a generalization: completely iterative algebras. The terminal coalgebra turns out to be the initial corecursive algebra as well as the initial completely iterative algebra. Dually, the initial algebra is the initial (parametrically) recursive coalgebra. These results explain the title of the chapter. We apply recursive coalgebras in order to obtain a new proof of the Initial Algebra Theorem from Chapter 6.