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nLab > Latest Changes: monoidal category

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    • CommentRowNumber101.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2023

    added publication data for this item:

    diff, v150, current

    • CommentRowNumber102.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2023
    • (edited Jun 4th 2023)

    added pointer to:

    diff, v154, current

  3. the change made removes the conditions (associativity and identities of morphisms) that are inherited directly from those of a category.

    naman

    diff, v159, current

    • CommentRowNumber104.
    • CommentAuthorUrs
    • CommentTimeOct 18th 2023

    Naman, I don’t see what is gained by your edit (here):

    All of the properties listed there follow from the previous discussion, the point is, as it says, to make it “very explicit”.

    The lines you removed serve that purpose. At the very least, absolutely no harm is done by keeping them.

    I think they should be reinstantiated.

    • CommentRowNumber105.
    • CommentAuthorJ-B Vienney
    • CommentTimeOct 18th 2023
    • (edited Oct 18th 2023)

    Naman: the conditions are not inherited from the definition of a functor or a category, so I reinstantiated them. They are exactly the conditions for a monoidal category to be strict. Like it was after your edit, the explicit definition was no longer correct.

    diff, v160, current

    • CommentRowNumber106.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2024

    added pointer to:

    • Jean Bénabou, Les catégories multiplicatives, Séminaire de mathématiquepure pure 27, Université de Louvain (1972) [pdf]

    diff, v162, current

  7. Added result of endomorphism monoid of unit to be commutative.

    diff, v163, current

  8. Unnecessary extra parentheses

    Olivia Borghi

    diff, v164, current

  9. Added to the existing section on representable multicategories that maps between underlying representable multicategories correspond to lax monoidal functors.

    Added that the category of monoidal categories and monoidal functors is equivalent to the category representable colored PROs.

    Aaron David Fairbanks

    diff, v165, current

    • CommentRowNumber110.
    • CommentAuthorJohn Baez
    • CommentTimeJul 19th 2024

    Added remark that Benabou’s early definition of monoidal category is incorrect, and link to a paper explaining why.

    diff, v169, current

    • CommentRowNumber111.
    • CommentAuthorvarkor
    • CommentTimeAug 23rd 2024

    Added a reference to an alternative axiomatisation of monoidal categories.

    diff, v170, current

    • CommentRowNumber112.
    • CommentAuthorUalrus
    • CommentTimeNov 5th 2024

    Hello everyone,

    In the subsection of internal logic I’m pretty sure that should be the internal language of a closed monoidal category instead of a monoidal category. The internal language of a monoidal category should be more akin to that of algebraic type theory but taking care of structural rules.

    I’m not familiar with editing the nlab nor do I feel extremely confident in what I’m saying so instead I’m posting here.

    Cheers!

101 to 112 of 112

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