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I find the page lax monoidal transformation confusing. To me, a “monoidal transformation” is a natural transformation between monoidal functors which is compatible with the monoidal structure (and there is no room for such a thing to be lax or colax). I would call the structure described on that page something like a “monoidal structure map”.
Sounds good. I have changed it accordingly.
Is this called the “lax monoidal transformation” in the literature? If so, then we should still mention that and explain what’s wrong with it.
I think I created that entry when I wrote monoidal Dold-Kan correspondence and related entries. In that context for instance the article
Schwede, Shipley, Equivalences of monoidal model categories (pdf)
uses the term this way (page 5-6).
I’ve put that in.
Great, thanks. The page lax monoidal transformation still seems to exist; is that the cache acting weird?
Yep, that’s the cache bug. (I can’t clear it from here.) But it’s lasting a longer time that it used to.
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