Many usual functors are defined by right modules over operads. In this chapter we study the universal constructions of §4: enveloping operads (§10.1), enveloping algebras (§10.2), and Kähler differentials (§10.3).
In §§10.2-10.3, we apply the principle of generalized point-tensors to extend constructions of §4 in order to obtain structure results on the modules which represent the enveloping algebra and Kähler differential functors. The examples of these sections are intended as illustrations of our constructions.
In §17, we study other constructions which occur in the homotopy theory of algebras over operads: cofibrant replacements, simplicial resolutions, and cotangent complexes. New instances of functors associated to right modules over operads can be derived from these examples by using categorical operations of §6, §7 and §9.
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© 2009 Springer-Verlag Berlin Heidelberg
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Fresse, B. (2009). Miscellaneous examples. 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_10
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DOI: https://doi.org/10.1007/978-3-540-89056-0_10
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