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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 11th 2011
    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeFeb 12th 2011

    You defined “has adjoints” twice. It seems to me that the first should have been for 11-morphisms and I changed it accordingly.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 12th 2011

    Something I may have asked before, but we seem to deal with \infty-categories with various properties assigned to certain intervals of nn-morphisms; no property, has duals, is invertible, is trivial. So we may say ’invertible above nn’, or ’trivial above n+kn + k and below kk perhaps with duals between. How far do they ever get combined? I see we have k-tuply monoidal (n,r)-category. Do they crop up in nature? How about a k-tuply monoidal (infinity,n)-category with duals?

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeFeb 13th 2011

    I see we have k-tuply monoidal (n,r)-category. Do they crop up in nature?

    I mostly only wrote that to record the insight that the concept still makes sense when r=1r = -1 (giving the concept of kk-tuply groupal nn-groupoid).

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2011

    kk-tuply monoidal (n,r)(n,r)-categories certainly crop up in nature! How could they not?