Free iterative theories: a coalgebraic view

• DOI: 10.1017/s0960129502003924
• Publication Date: 2003-04-04T11:19:34Z
• Authors: JIR˘Í ADÁMEK; STEFAN MILIUS; JIR˘Í VELEBIL
• Keywords: 0102 computer and information sciences; 01 natural sciences

Every finitary endofunctor of $\Set$ is proved to generate a free iterative theory in the sense of Elgot. This work is based on coalgebras, specifically on parametric corecursion, and the proof is presented for categories more general than just $\Set$.