Pith. Sign in

RECORD

Derived A-infinity algebras in an operadic context

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Muriel Livernet, Constanze Roitzheim, Sarah Whitehouse

Algebraic Topology · Submitted 24 Oct 2011

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

The authors' main claim We explain how derived A-infinity algebras can be viewed as algebras over an operad.

how it is stated · asserted 0.97 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1110.5167 (version 3)
Pith IDW5IXISLL, Pith's permanent record of this paper and its review
CitationConstanze Roitzheim, Muriel Livernet, Sarah Whitehouse. "Derived A-infinity algebras in an operadic context." arXiv:1110.5167 (2011). https://pith.science/paper/W5IXISLL
Claim paper

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,486 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Derived A-infinity algebras were developed recently by Sagave. Their advantage over classical A-infinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A-infinity algebras can be viewed as algebras over an operad. More specifically, we describe how this operad arises as a resolution of the operad dAs encoding bidgas. This generalises the established result describing the operad A-infinity as a resolution of the operad As encoding associative algebras. We further show Sagave's definition of morphisms agrees with the infinity-morphisms of dA-infinity algebras arising from operadic machinery. We also study the operadic homology of derived A-infinity algebras.

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 Derived A-infinity algebras were developed recently by Sagave. background 1.00 0.03 0.04 asserted 1.00
s1 Their advantage over classical A-infinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. background 0.93 0.08 0.09 asserted 1.00
s2 We explain how derived A-infinity algebras can be viewed as algebras over an operad. contribution 0.98 0.93 0.26 asserted 0.97
s3 More specifically, we describe how this operad arises as a resolution of the operad dAs encoding bidgas. contribution 0.87 0.92 0.19 asserted 1.00
s4 This generalises the established result describing the operad A-infinity as a resolution of the operad As encoding associative algebras. interpretation 0.40 0.29 0.20 asserted 1.00
s5 We further show Sagave's definition of morphisms agrees with the infinity-morphisms of dA-infinity algebras arising from operadic machinery. result 0.76 0.92 0.18 asserted 1.00
s6 We also study the operadic homology of derived A-infinity algebras. contribution 1.00 0.94 0.08 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

Derived A-infinity algebras were developed recently by Sagave. Their advantage over classical A-infinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A-infinity algebras can be viewed as algebras over an operad. More specifically, we describe how this operad arises as a resolution of the operad dAs encoding bidgas. This generalises the established result describing the operad A-infinity as a resolution of the operad As encoding associative algebras. We further show Sagave's definition of morphisms agrees with the infinity-morphisms of dA-infinity algebras arising from operadic machinery. We also study the operadic homology of derived A-infinity algebras.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.