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 $(-)^{\mathbf{2}}$ on Cat in the light of the no-iteration description of the algebras.
Keywords: Pseudomonad, algebras
2010 MSC: 18B35, 06D10, 06B23
Theory and Applications of Categories, Vol. 28, 2013, No. 14, pp 371-402.
Published 2013-07-01.
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