2017/03/22 by Adámek, Jiří, Milius, Stefan
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1703.07574
For an endofunctor H on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on Y as the coproduct of the final coalgebra for H and the free H-algebra on Y. As a consequence, we derive that H is a cia functor, i.e., its corecursive algebras are precisely the cias (completely iterative algebras). Also all functors H(-) + Y are then cia functors. For finitary set functors we prove that, conversely, if H is a cia functor, then it has the form H = W × (-) + Y for some sets W and Y.