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An analogue of Stone duality via support

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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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Henning Krause

Category Theory · Submitted 23 Jul 2023

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

The authors' main claim The notion of support provides an analogue of Stone duality, relating lattices to topological spaces.

how it is stated · asserted 1.00 read the record →

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arXiv ID2307.12391 (version 1)
Pith IDAA2K7L7H, Pith's permanent record of this paper and its review
CitationHenning Krause. "An analogue of Stone duality via support." arXiv:2307.12391 (2023). https://pith.science/paper/AA2K7L7H
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,464 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.65 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. As an application we indicate some consequences for tensor exact categories.

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 The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. background 0.53 0.34 0.70 asserted 1.00
s1 This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. contribution 0.93 0.41 0.07 asserted 0.82
s2 In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. contribution 0.78 0.44 0.12 asserted 0.96
s3 As an application we indicate some consequences for tensor exact categories. contribution 0.42 0.79 0.11 hedged possibility 0.98

What kind of paper the classifier reports this is: theoretical result 0.45 · evidence from argument 0.61.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
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

The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. As an application we indicate some consequences for tensor exact categories.

Human review

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How the literature uses it

1 arXiv paper cite this in 1 sentence

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

What it cites · 2 sentences without a confident label

Cites as background 2 papers
  • More recent work focusses on support for triangulated categories, without assuming a tensor product, or at least without assuming it to be symmetric [ref] .

    Approximating triangulated categories by spaces · Introduction · 0.96

  • More recent work focusses on support for triangulated categories, without assuming a tensor product, or at least without assuming it to be symmetric [ref] .

    Central support for triangulated categories · Introduction · 0.96

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