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A categorical equivalence for odd or even involutive FL$_e$-chains

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Sándor Jenei

Category Theory · Submitted 6 Apr 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups.

how it is stated · asserted 1.00 read the record →

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arXiv ID2304.03008 (version 2)
Pith IDJPDKVWZW, Pith's permanent record of this paper and its review
CitationS\'andor Jenei. "A categorical equivalence for odd or even involutive FL$_e$-chains." arXiv:2304.03008 (2023). https://pith.science/paper/JPDKVWZW
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,344 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups. Restricting this equivalence only to odd or only to even involutive FL$_e$-chains or to further subclasses thereof (e.g., to Sugihara chains) yields further categorical equivalences.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups. result 0.60 0.94 0.92 asserted 1.00
s1 Restricting this equivalence only to odd or only to even involutive FL$_e$-chains or to further subclasses thereof (e.g., to Sugihara chains) yields further categorical equivalences. result 0.65 0.80 0.13 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups. Restricting this equivalence only to odd or only to even involutive FL$_e$-chains or to further subclasses thereof (e.g., to Sugihara chains) yields further categorical equivalences.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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