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Generalized Operads and Their Inner Cohomomorphisms

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Geometry and Dynamics of Groups and Spaces

Part of the book series: Progress in Mathematics ((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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, USA

    Dennis V. Borisov & Yuri I. Manin

  2. Max-Planck-Institut für Mathematik, Bonn, Germany

    Yuri I. Manin

Authors
  1. Dennis V. Borisov
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  2. Yuri I. Manin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT, 06520, USA

    Mikhail Kapranov

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Yuri Ivanovich Manin  & Pieter Moree  & 

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka, 3, 01601, Kyiv, Ukraine

    Sergiy Kolyada

  4. UFR de Mathématiques, Université de Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Leonid Potyagailo

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Borisov, D.V., Manin, Y.I. (2007). Generalized Operads and Their Inner Cohomomorphisms. In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_4

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