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

    Anonymous

    v1, current

  2. The categorification of a magma

    Anonymous

    v1, current

    • 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).

    diff, v3, current

    • 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 ρ I=λ I\rho_I = \lambda_I

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 7th 2021

    Added example of Ackermann groupoids.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 7th 2021

    However, I do wonder if one should ask that ρ I=λ I\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 IIII\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.

    diff, v5, current

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