A foundation for PROPs, algebras, and modules / Donald Yau, Mark W. Johnson.

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PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fiel...

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Bibliographic Details
Main Authors: Yau, Donald Y. (Donald Ying), 1977- (Author), Johnson, Mark W., 1973- (Author)
Language:English
Published: Providence, Rhode Island : American Mathematical Society, [2015]
Series:Mathematical surveys and monographs ; v. 203.
Subjects:
Permutation groups.
Categories (Mathematics)
Modules (Algebra)
Category theory; homological algebra > Categories with structure > None of the above, but in this section.
Algebraic topology > Applied homological algebra and category theory > Topological categories, foundations of homotopy theory.
Commutative algebra > Homological methods > Deformations and infinitesimal methods.
Quantum theory > Quantum field theory; related classical field theories > String and superstring theories; other extended objects (e.g., branes)
Physical Description:xxxi, 311 pages : illustrations ; 26 cm.
Format: Book
Contents:
  • Part 1. Wheeled graphs and pasting schemes. Wheeled graphs
  • Special sets of graphs
  • Basic operations on wheeled graphs
  • Graph groupoids
  • Graph substitution
  • Properties of graph substitution
  • Generators of graphs
  • Pasting schemes
  • Well-matched pasting schemes
  • Part 2. Generalized PROPs, algebras, and modules. Generalized PROPs
  • Biased characterizations of generalized PROPs
  • Functors of generalized PROPs
  • Algebra over generalized PROPs
  • Alternative descriptions of generalized PROPs
  • Modules over generalized PROPs
  • May modules over algebras over operads.