Added some relationships between various categories of monoidal categories.

Aaron David Fairbanks

]]>Unclear what “calvin lee” in #13 really did. The edit history shows no change (so he might have edited the redirects or the like, which isn’t caught by the edit history).

]]>added pointer to:

- Samuel Eilenberg, G. Max Kelly, p. 473 in:
*Closed Categories*, in: S. Eilenberg, D. K. Harrison, S. MacLane, H. Röhrl (eds.):*Proceedings of the Conference on Categorical Algebra - La Jolla 1965*, Springer (1966) 421-562 [doi:10.1007/978-3-642-99902-4]

calvin lee

]]>added pointer to:

- Samuel Eilenberg, G. Max Kelly, p. 473 in:
*Closed Categories*, in: S. Eilenberg, D. K. Harrison, S. MacLane, H. Röhrl (eds.):*Proceedings of the Conference on Categorical Algebra - La Jolla 1965*, Springer (1966) 421-562 [doi:10.1007/978-3-642-99902-4]

added pointer to:

- Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik, §2.4 in :
*Tensor Categories*, AMS Mathematical Surveys and Monographs**205**(2015) [ISBN:978-1-4704-3441-0, pdf]

added pointer to:

- Saunders MacLane, §XI.2 of:
*Categories for the Working Mathematician*, Graduate Texts in Mathematics**5**Springer (second ed. 1997) [doi:10.1007/978-1-4757-4721-8]

x-ref with the article on change of base for enriched categories

]]>Changed a little bit the presentation of the definition by distinguishing the functor and the coherence maps

]]>replaced “identities” with “identity morphisms” (here)

]]>Define strict monoidal functors. There is an existing redirect for this term, but it was not defined.

]]>Is the definition of

lax monoidal functor between monoidalin the sense of Gordon–Power–Street already documented on the nLab?bicategories

It seems that this is not the case.

monoidal functor appears to be about monoidal categories only.

And that’s how it should be. The concept for monoidal 2-categories should go under *monoidal 2-functor*.

Is the definition of *lax monoidal functor between monoidal bicategories* in the sense of Gordon–Power–Street already documented on the nLab?

Remarks. monoidal functor appears to be about monoidal categories only. Motivation is partly studying Chapter 13 of Garner–Shulman Adv Math 289.

]]>The definition at *monoidal functor* used to be stated without the associators, but then there were a dozen lines of commentary on how to put them in.

Now I have just put them in. :-)

]]>Ah, I thought better of it and have everything now just at monoidal functor

]]>created (finally) lax monoidal functor (redirecting monoidal functor to that) and strong monoidal functor.

Hope I got the relation to 2-functors right. I remember there was some subtlety to be aware of, but I forget which one. I could look it up, but I guess you can easily tell me.

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