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arXiv · 0907.1359

On the formal theory of pseudomonads and pseudodistributive laws

Nicola Gambino·Gabriele Lobbia
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Abstract

We contribute to the formal theory of pseudomonads, i.e. the analogue for pseudomonads of the formal theory of monads. In particular, we solve a problem posed by Steve Lack by proving that, for every Gray-category K, there is a Gray-category Psm(K) of pseudomonads, pseudomonad morphisms, pseudomonad transformations and pseudomonad modifications in K. We then establish a triequivalence between Psm(K) and the Gray-category of pseudomonads introduced by Marmolejo. Finally, these results are applied to give a clear account of the coherence conditions for pseudodistributive laws. 41 pages. Comments welcome.

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Nicola Gambino, Gabriele Lobbia. 2009-07-08. On the formal theory of pseudomonads and pseudodistributive laws. https://arxiv.org/abs/0907.1359

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