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Generalized Operads and Their Inner Cohomomorphisms

  • Dennis V. Borisov
  • Yuri I. Manin
Part of the Progress in Mathematics book series (PM, volume 265)

Abstract

In this paper we introduce a notion of generalized operad containing as special cases various kinds of operad-like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories (and categories of algebras over them). We argue that they provide an approach to symmetry and moduli objects in non-commutative geometries based upon these “ring-like” structures. We give a unified axiomatic treatment of generalized operads as functors on categories of abstract labeled graphs. Finally, we extend inner cohomomorphism constructions to more general categorical contexts.

Keywords

Operads algebras inner cohomomorphisms symmetry and deformations in noncommutative geometry 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Dennis V. Borisov
    • 1
  • Yuri I. Manin
    • 1
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Max-Planck-Institut für MathematikBonnGermany

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