The usual constructions of module categories (namely free objects, extension and restriction of structures) make sense in the context of right modules over operads. In this chapter we check that these constructions correspond to natural operations on functors.
In §7.1, we determine the functor associated to free objects in right modules over operads. Besides, we observe that the category of right modules over an operad R is equipped with small projective generators defined by the free objects associated to the generating Σ∗-objects Fr = I?r, r ? N, and we determine the associated functors on R-algebras.
In §7.2, we define the extension and restriction functors for right modules over operads and we make explicit the corresponding operations on functors.
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© 2009 Springer-Verlag Berlin Heidelberg
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Fresse, B. (2009). Universal constructions on right modules over operads. 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_7
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DOI: https://doi.org/10.1007/978-3-540-89056-0_7
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