Questions tagged [operads]

Operads are structures encoding the properties of algebras (in a very general sense), for example associativity, commutativity, unitality, and the relations between them. Their main uses lie in (abstract-algebra), (category-theory) or (algebraic-topology).

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The construction of free symmetric/non-symmetric operads

I have a couple of questions concerning basic notions in operad theory. What is the ideological difference between symmetric and non-symmetric operads? I think about the difference in the following way. Symmetric operads are collections of boxes…
Gregg
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Symmetric and non-symmetric operads

I have trouble understanding why they are distinct notions of symmetric operad and non-symmetric operads : are they really both needed ? It seems like symmetric operads are more general, but I do not understand why we just could not forget about the…
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What is the meaning of some concepts in Operads?

I have already studied the notion of Operads. As I am new in this way, I need some clarification of basic concepts related to Operas through examples. We have the following notation: $\sum$: a set of symbols of algebraic operations $f$ together…
Nil
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Projection onto the Homology of an operad

Suppose that $\mathcal{O}$ is a differential graded operad over a field and that $H(\mathcal{O})$ (i.e. taking the arity wise homology) is an operad, too. (If possible, I would avoid to restrict to symmetric operads) Is the natural projection $\pi :…
Mark Neuhaus
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