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I'm not sure what the question you're trying to ask is, but the answer to the question that you have asked is that an operad automorphism is an invertible operad endomorphism.

[EDIT] (just restating Ryan's comment on the original post) An operad endomorphism is an operad morphism where the source and target operads are the same. An operad morphism is a collection of maps $\mathcal{O}(n)\rightarrow\mathcal{P}(n)$, one for each arity, such that the obvious squares involving the operad structure maps commute. [/EDIT]

Perhaps you want to know about operad automorphisms in a homotopy category. In that case you want to understand what an operad quasi-isomorphism is. This is an operad morphism which is a quasi-isomorphism on each underlying space of operations.

Would you like to refine the question?

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I'm not sure what the question you're trying to ask is, but the answer to the question that you have asked is that an operad automorphism is an invertible operad endomorphism.

Perhaps you want to know about operad automorphisms in a homotopy category. In that case you want to understand what an operad quasi-isomorphism is. This is an operad morphism which is a quasi-isomorphism on each underlying space of operations.

Would you like to refine the question?