Metraipolis › archive › dc_8024def806e2

Final coalgebras over R-modules — arXiv:2611.03174

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03174
License (as archived): CC0-1.0
Archived: 2026-11-03T18:59:10.407Z
SHA-256 of the archived text: 0e1770d88c8f64c2f11573663a1c27bf3dbd4e2c2bcfc56997581794b39f9953
Stable URL of this page: https://metraipolis.com/documento/dc_8024def806e2

How to cite

Final coalgebras over R-modules — arXiv:2611.03174 — arXiv (en), https://arxiv.org/abs/2611.03174 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_8024def806e2 (Metraipolis archive dc_8024def806e2, sha256 0e1770d88c8f64c2f11573663a1c27bf3dbd4e2c2bcfc56997581794b39f9953)

BibTeX

@misc{dc8024def806e2,
  title = {Final coalgebras over R-modules — arXiv:2611.03174},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03174},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_8024def806e2; sha256 0e1770d88c8f64c2f11573663a1c27bf3dbd4e2c2bcfc56997581794b39f9953},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03174. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Final coalgebras and the coinduction principle for coalgebras over $R$-modules, where $R$ is a commutative ring, are essential in determining the denotational behaviour of various types of linear weighted automata. The goal of this paper is to provide lower and upper bounds on the ordinals that are needed to construct final coalgebras over $R$-modules as the limit of a transfinite sequence of functor iterations. We give an example of a binary intersection preserving finitary functor on the category of abelian groups, which is the category of modules over integers, that fails to converge in $\omega \cdot 2$ steps, thus settling an open problem of Adámek, Milius, and Moss. Then we relate this to the failure of the Artinian property of the integers and show that all finitary functors on $R$-modules for a Noetherian ring $R$ with Krull dimension $n$, which preserve countable directed intersections and a generalised notion of monomorphism, converge in $\omega \cdot (n + 2)$ steps. We also establish how the connection between Aczel-Mendler bisimulation and behavioural equivalence is mediated by the functor $\operatorname{Ext}^1$. These results show that homological algebra tools can play an important role in coalgebra.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv cs.LO, nuovi lavori del giorno).
Categorie arXiv: Logic in Computer Science (cs.LO) ; Commutative Algebra (math.AC); Category Theory (math.CT).
Pagina del lavoro: https://arxiv.org/abs/2611.03174 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:18:22.757Z dalla pagina https://arxiv.org/list/cs.LO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).