Talk:Braided monoidal category

Braided category
Anybody willing to fill in this redlink, either by an appropriate redirect, or a new article? Oleg Alexandrov (talk) 07:11, 23 April 2006 (UTC)

I retract my comments I made May 9, 2007 on Wikipedia's article on Braided Monoidal Categories. D.S.

Question about usage of opposite category here
I think the usage of $$\mathcal{C}^{op}$$ in the first sentence is confusing. In particular, it seems like $$\mathcal{C}^{op}$$ is being described as the same category as $$\mathcal{C}$$ but with a different (opposite) monoidal structure, rather than a monoidal structure on the opposite category of $$\mathcal{C}$$ as described in Opposite (category theory), which is the much more customary definition of $$\mathcal{C}^{op}$$.

So, given a monoidal category, $$(\mathcal{C},\otimes)$$, are we saying that $$(\mathcal{C},\otimes)^{op}$$ is of the form $$(\mathcal{C}^{op},\otimes^{op})$$ or is it of the form $$(\mathcal{C},\otimes^{op})$$?

A "natural isomorphism" would mean between two functors between the same categories, so it seems like this would mean that you'd want $$\otimes^{op}:\mathcal{C}\times\mathcal{C}\rightarrow\mathcal{C}$$ and a natural isomorphism between $$\otimes$$ and $$\otimes^{op}$$.

Thomaso (talk) 18:03, 10 February 2012 (UTC)

I agree. I'm trying to work out if a few different characterisations are equal and the description given in the opening line is not exactly correct. The differences are subtle but it's best to be as exact as possible. I believe the natural isomorphism is from $$\otimes$$ to $$\otimes^{op}$$ as you say.

MitchB (talk) 04:04, 12 June 2013 (UTC)