Bases for parametrized iterativity

Jiří Adámek, Stefan Milius, Jiří Velebil
2008 Information and Computation  
Parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables (chosen as a parameter). We show how such algebras can be introduced in an arbitrary category A by employing a base, i.e., an operation interpreting objects of A as monads on A. For every base we prove that free base algebras and free iterative base algebras exist. The main result is a coalgebraic construction of the
more » ... atter: all equation morphisms form a diagram whose colimit is proved to be a free iterative base algebra. (Milius). 1 Finitary functors are those preserving filtered colimits. Finitary monads are monads with a finitary underlying functor. 0890-5401/$ -see front matter
doi:10.1016/j.ic.2008.05.002 fatcat:p42nvstz3zczfkavuknhce45l4