Hi all again, thanks to those who replied off-list. The canonical reference is Joyal–Street's Braided monoidal categories. (Someone else also pointed out that algebras for the E_2 operad are equivalent to E_1 algebras in the category of E_1 algebras.) However, my *actual* desired result is that the multiplication of a _symmetric_ monoidal category is a braided functor (i.e. commutes with the braiding=symmetry in this case). I proved this to my own satisfaction, but my proof is not very nice, and I'm searching for a cleaner verification of the required commuting diagram. Surely this was also known! And if so, what's a good reference (I expect it to be even earlier than Joyal–Street). Thanks, David PS this question relating to Lawvere's 2015 invited CT address might be of interest to people here: https://mathoverflow.net/questions/348436/the-barr-boole-galois-topos-a-modi... David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com On Wed, 11 Dec 2019 at 16:59, David Roberts <droberts.65537@gmail.com> wrote:
Hi all,
I have half convinced myself (without checking details) that if I have a braided monoidal category (C,@), then the monoidal product @: C x C --> C is strong monoidal. Is this true? What's a reference for this I could point to?
Thanks, David
David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com
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