Abstract. We present the no-iteration version of the coherence conditions necessary to define a pseudomonad, and a description of the algebras for it in a similar fashion. We show that every no-iteration pseudomonad induces a pseudomonad, and that the corresponding algebras are equivalent. We also show that every pseudomonad induces a no-iteration pseudomonad, and again, that the corresponding algebras are equivalent. We conclude with an analysis of the algebras for the 2-monad (−) 2 on Cat in the light of the no-iteration description of the algebras. 1
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