Free operads in differential graded modules. (Spanish. English summary) Zbl 1513.18014
Summary: Operads are algebraic structures who have manifested their importance in the study and classification of the homotopic properties of loop spaces. This paper makes a survey of the notion of free operad, both for the symmetric case and for the non-symmetric case, since this type of construction represents a valuable method in the design of operads in different situations. In order to do this, the symmetric operads are interpreted as monoids on the category of S-modules. This work has as objective to show some of the main properties between the functors associated with the constructions of free symmetric operads for understanding the mechanisms of this type of structure. Which leads to the main result of this paper, where the symmetric free operad functor is expressed in terms of the non-symmetric free operad functor, when the actions by the symmetric groups are free.
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