Iterative reflections of monads

@article{Admek2010IterativeRO,
  title={Iterative reflections of monads},
  author={Jir{\'i} Ad{\'a}mek and Stefan Milius and Jiri Velebil},
  journal={Mathematical Structures in Computer Science},
  year={2010},
  volume={20},
  pages={419 - 452}
}
Iterative monads were introduced by Calvin Elgot in the 1970's and are those ideal monads in which every guarded system of recursive equations has a unique solution. We prove that every ideal monad has an iterative reflection, that is, an embedding into an iterative monad with the expected universal property. We also introduce the concept of iterativity for algebras for the monad , following in the footsteps of Evelyn Nelson and Jerzy Tiuryn, and prove that is iterative if and only if all free… 
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8 Citations
Background Citations
3
Methods Citations
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8 Citations

Citation Type

Citation Type

A Description of Iterative Reflections of Monads (Extended Abstract)
TLDR
This paper proves that the monad of free commutative binary algebras is iterative in the sense of Calvin Elgot, and shows how to freely add unique solutions of recursive equations to a given algebraic theory.
How iterative reflections of monads are constructed
On second-order iterative monads
Recursive Program Schemes and Context-Free Monads
Completely iterative monads in semantics of coinductive programs
TLDR
The thesis of this dissertation is that the right kind of monads to describe the observable behaviour of programs are completely iterative monads (cims), introduced by Elgot and more recently studied by Adamek and others.
Elgot theories: a new perspective on the equational properties of iteration
TLDR
This paper shows that in the coalgebraic approach to iteration, the more appropriate concept is that of a functorial iteration theory (called Elgot theory), which is proved to be monadic over the category of sets in context.
Elgot Theories: A New Perspective of Iteration Theories (Extended Abstract)
Equational properties of iterative monads

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