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arxiv: math/0404016 · v1 · submitted 2004-04-01 · 🧮 math.CT · math.AT· math.QA

Are operads algebraic theories?

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keywords algebraicoperadsisomorphicpairtheoriesalthoughcannotexhibit
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I exhibit a pair of non-symmetric operads that, although not themselves isomorphic, induce isomorphic monads. The existence of such a pair implies that if `algebraic theory' is understood as meaning `monad', operads cannot be regarded as algebraic theories of a special kind.

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