Added related concepts:

Removed several duplicates and rearranged the list.

]]>Added: every monoidal category is equivalent to a skeletal strict monoidal one. (FinSet, $\times$) is, but (Set, $\times$) is not.

]]>I mean whiskering. But just convince yourself that given a commuting triangle of isomorphisms, there is a corresponding commuting triangle with the direction of any one of the arrows reversed and labeled by the inverse of the original morphism. It’s immediate, by the definition of inverse morphisms.

]]>[ duplicate removed ]

]]>Given a commuting diagram with an isomorphism, whiskering it with the inverse of that isomorphism gives a commuting diagram of the same shape as before but with that one arrow now pointing in the opposite direction.

Now once the perimeter of that big diagram commutes apply this reversal to the top right morphism. The resulting top right triangle is then seen to commute, and hence so does the original triangle in question.

]]>Added to the Idea section the fact that monoidal categories can be considered as one-object bicategories (and added relevant material to bicategory, under the Examples section).

]]>Not according to mine.

]]>The last revision was March 30, 2020 according to the history page. ]]>

I added a few words; does that help?

]]>In enriched category, section "2 -Definition", it is written that "one may think of a monoidal category as a bicategory with a single object".

Is it possible to add a sentence about this in this page ? ]]>

Yes, I think you’re right. Why don’t you fix it?

]]>It seems to me like the parens are misplaced on one of the terms. ]]>

This looks good to me, thanks.

]]>latex fix

]]>Mention earlier in the definition section that a monoidal category is just a category. Also add paragraph about how the definition of the monoidal structure of a category relies on the monoidal structure of the parent 2-category, in accordance with the microcosm principle. See discussion at https://nforum.ncatlab.org/discussion/11003/if-defining-monoidal-category-as-monoid-is-circular-then-sos-our-definition-of-monoidal-category/

]]>It seems to me that the facets of the 4-simplex oriental are the edges, not the vertices, of the pentagon identity.

DavidMJC

]]>Number the last natural isomorphism in this definition.

relrod

]]>Thanks for raising this, deleted these revisions from September now, and blocked the IP address as well in nginx, because it has been used consistently.

I actually don’t know how the author managed to get those edits through; my attempts to reproduce the spam result in the spam filter blocking the edits correctly. It is possible that I misread the date to be from an earlier year than this year (i.e. it was just something that I forgot to clear up).

]]>The page Mac+Lane’s+proof+of+the+coherence+theorem+for+monoidal+categories still contains links of similar type at the bottom.

]]>Have now cleared up everything with

```
1337777.OOO
```

with the HTML character in the middle, including some older pages. There exist some historical ones (only in revision history I think) without the HTML character in the middle, I’ll try to remove those tomorrow.

I’ve also tightened the spam filter a little further.

Thanks very much for the alert, Rod!

]]>