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Monoidal Properties of Franke's Exotic Equivalence

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Nikitas Nikandros, Constanze Roitzheim

Algebraic Topology · Submitted 23 Jan 2023

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

The authors' main claim We show that, while not being a tensor-triangulated functor in general, R is compatible with monoidal products.

how it is stated · asserted 1.00 read the record →

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arXiv ID2301.09432 (version 2)
Pith IDHNXKRM5P, Pith's permanent record of this paper and its review
CitationConstanze Roitzheim, Nikitas Nikandros. "Monoidal Properties of Franke's Exotic Equivalence." arXiv:2301.09432 (2023). https://pith.science/paper/HNXKRM5P
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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, 2,299 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.85 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.57 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Franke's reconstruction functor R is known to provide examples of triangulated equivalences between homotopy categories of stable model categories, which are exotic in the sense that the underlying model categories are not Quillen equivalent. We show that, while not being a tensor-triangulated functor in general, R is compatible with monoidal products.

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 Franke's reconstruction functor R is known to provide examples of triangulated equivalences between homotopy categories of stable model categories, which are exotic in the sense that the underlying model categories are not Quillen equivalent. background 1.00 0.04 0.05 asserted 1.00
s1 We show that, while not being a tensor-triangulated functor in general, R is compatible with monoidal products. result 0.92 0.95 0.88 asserted 1.00

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

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
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  • 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

Franke's reconstruction functor R is known to provide examples of triangulated equivalences between homotopy categories of stable model categories, which are exotic in the sense that the underlying model categories are not Quillen equivalent. We show that, while not being a tensor-triangulated functor in general, R is compatible with monoidal products.

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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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