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  • Appendix C - Set Functors

  • 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 552-597

  • Summary

    A set functor is an endofunctor on the category of sets. Although the topic of set functors is quite large, there are few if any chapter-length summaries directed to a researcher in the area of this book. This appendix collects the results on set functors that such a person ought to know, including the main preservation properties, such as preservation of weak pullbacks and of finite intersections. It contains the main examples of set functors used in the recent literature and a chart of their preservation properties. Studying monoid-valued functors, it connects the preservation properties of the functor to algebraic properties of the monoid. It presents Trnkova’s modification of a set functor at the empty set needed to obtain a functor preserving all finite intersections.