Are operads algebraic theories?

Tom Leinster

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arXiv · math/0404016

Are operads algebraic theories?

Tom Leinster

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Abstract

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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Tom Leinster. 2004-04-01. Are operads algebraic theories?. https://arxiv.org/abs/math/0404016

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