On Well-Founded and Recursive Coalgebras [chapter]

Jiří Adámek, Stefan Milius, Lawrence S. Moss
2020 Lecture Notes in Computer Science  
This paper studies fundamental questions concerning categorytheoretic 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
more » ... l Recursion Theorem that every wellfounded coalgebra is recursive, and we study conditions which imply the converse. In addition, we present a new equivalent characterization of well-foundedness: a coalgebra is well-founded iff it admits a coalgebra-toalgebra morphism to the initial algebra.
doi:10.1007/978-3-030-45231-5_2 fatcat:x376nvmz75bfvekoy7gva4ivhm