Talk:Closed monoidal category

Maybe Monoidal closed category is the more common term? Geometry guy 21:01, 14 May 2007 (UTC)

Notation

Does anyone have a reference for the notation used in this article? I'm suspicious of the notation $A\Leftarrow -$ for the right adjoint to $-\otimes A$. In the case of Set this would make $A\Leftarrow B$ the set of functions from A to B!? It seems like $-\Leftarrow A$ would be better.

In any case, I would prefer to switch notation to that used in the reference by Kelly. He uses $[A, -]$ for the right adjoint to $-\otimes A$ and $[\![A,-]\!]$ for the right adjoint to $A\otimes -$. This notational appears to be slightly more common. It's also consistent with the notation used at closed category. Any thoughts? -- Fropuff (talk) 00:25, 15 February 2008 (UTC)

Your first question has an easy answer: I made a typo when writing that section, which I've fixed now. It's vastly more common to use lollipop-shaped symbols than to use $\Leftarrow$ or $\Rightarrow$, especially in linear logic, but I'm not sure how get those symbols here.

I like $[A, B]$ for the internal hom in symmetric or braided monoidal categories, and that notation is indeed very common. But I don't think that using $[A,B]$ versus $[\![A,B]\!]$ makes the right/left distinction clear, in the cases where that distinction really matters, and I don't think it's caught on. John Baez (talk) 16:46, 7 August 2009 (UTC)