On functors preserving coproducts and algebras with iterativity

Journal article


Publication Details

Author(s): Adamek J, Milius S
Journal: Theoretical Computer Science
Publication year: 2019
Volume: 763
Pages range: 66-87
ISSN: 0304-3975


Abstract

An algebra for a functor H is called completely iterative (cia, for short) if every flat recursive equation in it has a unique solution. Every cia is corecursive, i.e., it admits a unique coalgebra-to-algebra morphism from every coalgebra. If the converse also holds, H is called a cia functor. We prove that whenever the base category is hyper-extensive (i.e. countable coproducts are 'well-behaved') and H preserves countable coproducts, then H is a cia functor. Surprisingly few cia functors exist among standard finitary set functors: in fact, the only ones are those preserving coproducts; they are given by X bar right arrow W x (-) + Y for some sets W and Y. (C) 2019 Elsevier B.V. All rights reserved.


FAU Authors / FAU Editors

Milius, Stefan apl. Prof. Dr.
Lehrstuhl für Informatik 8 (Theoretische Informatik)


External institutions with authors

Czech Technical University in Prague / České vysoké učení technické v Praze


How to cite

APA:
Adamek, J., & Milius, S. (2019). On functors preserving coproducts and algebras with iterativity. Theoretical Computer Science, 763, 66-87. https://dx.doi.org/10.1016/j.tcs.2019.01.018

MLA:
Adamek, Jiri, and Stefan Milius. "On functors preserving coproducts and algebras with iterativity." Theoretical Computer Science 763 (2019): 66-87.

BibTeX: 

Last updated on 2019-26-03 at 00:08