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• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeMay 31st 2018

Created, with so far just an overview of all the possibilities.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeMay 31st 2018

It would be nice to add a link to monoidal category which is currently still spam-locked…

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeMay 31st 2018

List some related notions and special cases.

• CommentRowNumber4.
• CommentAuthorRichard Williamson
• CommentTimeJul 16th 2018
• (edited Jul 16th 2018)

I have now removed the lock on editing the page monoidal category. The commit can be seen on github. I made a trivial edit and then another one to put the page back as it was before, to test that editing was now possible.

• CommentRowNumber5.
• CommentAuthorJohn Baez
• CommentTimeDec 20th 2020

Added reference to Bourke-Lack paper “Skew monoidal categories and skew multicategories”.

• CommentRowNumber6.
• CommentAuthormaxsnew
• CommentTimeDec 21st 2020

On the part about oplax monoidal categories, what does “weakly representable” mean? Does it mean satisfying the existence but not uniqueness part of representability (in type theory terminology $\beta$ but not $\eta$)? Is there an appropriate link?

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeJan 6th 2021

It means the morphism only satisfies a universal property (with an ordinary isomorphism) for multimorphisms without extra objects added on each side. See for instance section 9 of http://tac.mta.ca/tac/volumes/24/21/24-21abs.html.

• CommentRowNumber8.
• CommentAuthormattecapu
• CommentTimeAug 3rd 2022

add redirects for skew-monoidal