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Gerstenhaber-Schack diagram cohomology from operadic point of view

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Martin Doubek

Algebraic Topology · Submitted 10 Jan 2011

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

The authors' main claim We use this principle to prove that the Gerstenhaber-Schack diagram cohomology is operadic cohomology.

how it is stated · asserted 1.00 read the record →

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arXiv ID1101.1896 (version 1)
Pith IDYW44P7AX, Pith's permanent record of this paper and its review
CitationMartin Doubek. "Gerstenhaber-Schack diagram cohomology from operadic point of view." arXiv:1101.1896 (2011). https://pith.science/paper/YW44P7AX
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,304 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.24 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We show that the operadic cohomology for any type of algebras over a non-symmetric operad A can be computed as Ext in the category of operadic A-modules. We use this principle to prove that the Gerstenhaber-Schack diagram cohomology is operadic cohomology.

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 show that the operadic cohomology for any type of algebras over a non-symmetric operad A can be computed as Ext in the category of operadic A-modules. result 0.76 0.88 0.29 asserted 1.00
s1 We use this principle to prove that the Gerstenhaber-Schack diagram cohomology is operadic cohomology. result 0.72 0.94 0.67 asserted 1.00

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

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • T body sentences
  • C citations
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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 show that the operadic cohomology for any type of algebras over a non-symmetric operad A can be computed as Ext in the category of operadic A-modules. We use this principle to prove that the Gerstenhaber-Schack diagram cohomology is operadic cohomology.

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