On Well-Founded and Recursive Coalgebras
Abstract
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving endofunctors on complete and well-powered categories every coalgebra has a well-founded part, and we provide a new, shorter proof that this is the coreflection in the category of all well-founded coalgebras. We present a new more general proof of Taylor's General Recursion Theorem that every well-founded coalgebra is recursive, and we study under which hypothesis the converse holds. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-to-algebra morphism to the initial algebra.
Keywords
Cite
@article{arxiv.1910.09401,
title = {On Well-Founded and Recursive Coalgebras},
author = {Jiří Adámek and Stefan Milius and Lawrence S. Moss},
journal= {arXiv preprint arXiv:1910.09401},
year = {2020}
}