Abstract
For algebras A whose type is given by an endofunctor, iterativity means that every flat equation morphism in A has a unique solution. In our previous work we proved that every object generates a free iterative algebra, and we provided a coalgebraic construction of those free algebras.Iterativity w.r.t. an endofunctor was generalized by Tarmo Uustalu to iterativity w.r.t. a “base”, i.e., a functor of two variables yielding finitary monads in one variable. In the current paper we introduce iterative algebras in this general setting, and provide again a coalgebraic construction of free iterative algebras.
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