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Symmetric objects and functors

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1967)

In this chapter, we recall the definition of the category of Σ∗-objects and we review the relationship between Σ∗-objects and functors. In short, a Σ∗-object (in English words, a symmetric sequence of objects, or simply a symmetric object ) is the coefficient sequence of a generalized symmetric functor S(M) : X→ S(M,X), defined by a formula of the form In §2.1, we recall the definition of the tensor product of Σ∗-objects, the operation which reflects the pointwise tensor product of functors and which provides the category of Σ∗-objects with the structure of a symmetric monoidal category over the base category.

Keywords

  • Tensor Product
  • Symmetric Group
  • Monoidal Category
  • Monoidal Structure
  • Tensor Power

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2009 Springer-Verlag Berlin Heidelberg

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Fresse, B. (2009). Symmetric objects and functors. In: Modules over Operads and Functors. Lecture Notes in Mathematics(), vol 1967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89056-0_2

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