Operads are used to define categories of algebras, usually within a fixed underlying symmetric monoidal category C. But in the sequel, we form algebras in extensions of the category in which the operad is defined. Formally, we define algebras in symmetric monoidal categories E over the base category C.
In principle, we can use the functor η :C → E associated to the structure of a symmetric monoidal category over C to transport all objects in E. This functor maps an operad in C to an operad in E. Thus we could just change the underlying category to retrieve standard definitions.
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© 2009 Springer-Verlag Berlin Heidelberg
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Fresse, B. (2009). Operads and algebras in symmetric monoidal categories. 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_3
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DOI: https://doi.org/10.1007/978-3-540-89056-0_3
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