A logical analysis of fixpoint theorems
Category Theory
2022-11-04 v1
Abstract
We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially lower-semicontinuous. Sufficient conditions for the uniqueness of the fixpoint are established. Examples include known and new fixpoint theorems for metric spaces, fuzzy metric spaces, and probabilistic metric spaces.
Cite
@article{arxiv.2211.01782,
title = {A logical analysis of fixpoint theorems},
author = {Arij Benkhadra and Isar Stubbe},
journal= {arXiv preprint arXiv:2211.01782},
year = {2022}
}
Comments
preprint submitted for publication (16 pages)