Algebraic cocompleteness and finitary functors
Category Theory
2023-06-22 v5
Abstract
A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and, more generally, all precontinuous) set functors the initial algebra and terminal coalgebra are proved to carry a canonical partial order with the same ideal CPO-completion. And they also both carry a canonical ultrametric with the same Cauchy completion.
Cite
@article{arxiv.1903.02438,
title = {Algebraic cocompleteness and finitary functors},
author = {Jiří Adámek},
journal= {arXiv preprint arXiv:1903.02438},
year = {2023}
}