HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# Approximate Coalgebra Homomorphisms and Approximate Solutions

Abstract : Terminal coalgebras $\nu F$ of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their underlying sets. The subspace formed by the initial algebra $\mu F$ has the property that for every coalgebra A we obtain its unique homomorphism into $\nu F$ as a limit of a Cauchy sequence of morphisms into $\mu F$ called approximate homomorphisms. The concept of a strongly lfp category includes categories of sets, posets, vector spaces, boolean algebras, and many others.For the free completely iterative algebra $\varPsi B$ on a pointed object B we analogously present a canonical ultrametric on its underlying set. The subspace formed by the free algebra $\varPhi B$ on B has the property that for every recursive equation in $\varPsi B$ we obtain the unique solution as a limit of a Cauchy sequence of morphisms into $\varPhi B$ called approximate solutions. A completely analogous result holds for the free iterative algebra RB on B.
Document type :
Conference papers
Domain :
Complete list of metadata

https://hal.inria.fr/hal-03232353
Contributor : Hal Ifip Connect in order to contact the contributor
Submitted on : Friday, May 21, 2021 - 2:58:02 PM
Last modification on : Friday, May 21, 2021 - 3:05:03 PM
Long-term archiving on: : Sunday, August 22, 2021 - 6:49:35 PM

### File

##### Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed until : 2023-01-01

### Citation

Jiří Adámek. Approximate Coalgebra Homomorphisms and Approximate Solutions. 15th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2020, Dublin, Ireland. pp.11-31, ⟨10.1007/978-3-030-57201-3_2⟩. ⟨hal-03232353⟩

Record views