HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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
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

Please log in to resquest access to the document

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

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⟩

Share

Metrics

Record views

19