Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
426689 | Information and Computation | 2008 | 37 Pages |
Abstract
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 latter: all equation morphisms form a diagram whose colimit is proved to be a free iterative base algebra.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics