# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

1. Page created, but author did not leave any comments.

Anonymous

2. The categorification of a magma

Anonymous

• CommentRowNumber3.
• CommentAuthorvarkor
• CommentTimeMay 5th 2021

With reference to the terminology “monoidal category”, I think this ought to be called a “magmoidal category” (this appears to have been used more frequently in practice too).

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeMay 5th 2021

Changed name as suggested. I agree, it goes better with monoidal category, which is the categorification of a monoid, and appears in the literature: Davydov’s Nuclei of categories with tensor products and Lack and Street’s Triangulations, orientals, and skew monoidal categories, and honourable mention to H. Eades III in Introducing a New Project on The Combination of SubstructuralLogics and Dependent Type Theory (extended abstract).

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeMay 5th 2021

Also added example of “…with unit”, following Eades. This includes incoherent unitors, since there is no associator to be compatible with. However, I do wonder if one should ask that $\rho_I = \lambda_I$

• CommentRowNumber6.
• CommentAuthorDavidRoberts
• CommentTimeMay 7th 2021

• CommentRowNumber7.
• CommentAuthorvarkor
• CommentTimeMay 7th 2021

However, I do wonder if one should ask that $\rho_I = \lambda_I$

I agree that one should: as a term rewriting system, these rewrites should be convergent, so any choice of path should be equal.

• CommentRowNumber8.
• CommentAuthorDavidRoberts
• CommentTimeMay 12th 2021

Added note on a potentially necessary weak coherence condition for magmoidal categories with units, namely that there should be a unique coherence iso $I\otimes I \to I$, so the unitors should coincide. Also noted the usual unitor coherence condition can’t even be stated in the absence of associators.