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Jonas Frey (Dec 06 2024 at 13:08):Do the experts agree that the 8 coherence axioms in Marmolejo/Wood's No-Iteration Pseudomonads (Def. 2.1) are redundant? I think pseudomonads should have the same coherence theory -- and the 2 same axioms -- as monoidal categories (which seem to be their axioms 2 and 8), and Fiore/Gambino/Hyland/Winskel in Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures (Def 3.1) seem to agree.
Nathanael Arkor (Dec 06 2024 at 13:15):Yes, 3 of the 8 axioms are redundant. FGHW state this explicitly in Proposition 3.3. It is also observed in Lack and Street's On monads and warpings, as well as Walker's No-iteration pseudodistributive laws.
Nathanael Arkor (Dec 06 2024 at 13:17):(Similarly, one their axioms for pseudoalgebras is redundant, as observed in the Lack and Street paper.)
Jonas Frey (Dec 06 2024 at 13:25):Ahh I see, but axioms 4,6,7 are not redundant, but correspond to implicit naturality conditions in the FGHW paper. Thanks!