Back to Search
Start Over
On functors preserving coproducts and algebras with iterativity.
- Source :
-
Theoretical Computer Science . Apr2019, Vol. 763, p66-87. 22p. - Publication Year :
- 2019
-
Abstract
- 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 ↦ W × (−) + Y for some sets W and Y. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 763
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 134688346
- Full Text :
- https://doi.org/10.1016/j.tcs.2019.01.018