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A Koszul duality for props

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Bruno Vallette

Algebraic Topology · Submitted 24 Nov 2004

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

The authors' main claim In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0411542 (version 3)
Pith IDMLGXKCLU, Pith's permanent record of this paper and its review
CitationBruno Vallette. "A Koszul duality for props." arXiv:math/0411542 (2004). https://pith.science/paper/MLGXKCLU
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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, 2,266 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.49 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.

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 prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. background 1.00 0.05 0.03 asserted 1.00
s1 In this paper, we generalize the Koszul duality theory of associative algebras and operads to props. contribution 1.00 0.94 0.64 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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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

The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras and operads to props.

Human review

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References
How the literature uses it

10 arXiv papers cite this in 19 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

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 2 papers
  • We prove a Koszul duality theory for PROPs generalizing the one for associative algebras and for operads.

    Koszul duality for PROPs · 1.00

  • In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs.

    Dualite de Koszul des PROPs · 0.99

Papers citing it · 6 sentences without a confident label

Uses its method or tool 1 paper
  • This can be given explicitly by using the description of [ref] , keeping only the relations of genus zero.

    Properadic coformality of spheres · The dioperad $^(n)$ · 0.92

Compares with it 1 paper
  • Here we should mention that we use slightly different conventions as in [ref] , where it is assumed that the sets $C$ and $D$ are always non-empty, i.e., there is always at least one input and one output.

    Properads and Homotopy Algebras Related to Surfaces · Properads · 0.92

Cites it as background 8 papers
  • In [ref] he gives both an unbiased as well as a biased definition.

    Properads and Homotopy Algebras Related to Surfaces · Introduction · 0.90

  • The Koszul duality theory of properads, the associated deformation theory and the homotopy theory of algebras over a properad were respectively developed in [ref] , [ref] and [ref] .

    Kaledin classes and formality criteria · Recollections on properadic homological algebra · 1.00

  • Properads were introduced by Vallette [ref] , as a notion intermediate between operads and props, featuring important notions and results generalised from operads, such as Koszul duality.

    Graphs, hypergraphs, and properads · Introduction · 1.00

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