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Infinity Properads and Infinity Wheeled Properads pp 55–67Cite as

Properads

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2147))

Abstract

We recall both the biased and the unbiased definitions of a properad. The former describes a properad in terms of generating operations, namely, units, Σ-bimodule structure, and properadic composition. The unbiased definition of a properad describes it as an algebra over a monad induced by connected wheel-free graphs. The equivalence of the two definitions of a properad are proved in detail in Yau and Johnson (A Foundation for PROPs, Algebras, and Modules. Mathematical Surveys and Monographs, vol. 203, Am. Math. Soc., Providence, 2015) as an example of a general theory of generating sets for graphs.

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References

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Authors and Affiliations

  1. Stockholm University, Stockholm, Sweden

    Philip Hackney

  2. University of California, Los Angeles, CA, USA

    Marcy Robertson

  3. Ohio State University, Newark Campus, Newark, OH, USA

    Donald Yau

Authors
  1. Philip Hackney
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  2. Marcy Robertson
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  3. Donald Yau
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Hackney, P., Robertson, M., Yau, D. (2015). Properads. In: Infinity Properads and Infinity Wheeled Properads. Lecture Notes in Mathematics, vol 2147. Springer, Cham. https://doi.org/10.1007/978-3-319-20547-2_3

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